Papers

We consider the open XXZ spin chain with unparallel boundary fields, in the special case in which the Vertex-IRF transform of the K-matrix labelling the boundary field at site 1 is diagonal and invariant under the value of the gauge parameters, the other K-matrix being arbitrary. We discuss here several properties related to this special gauge invariant boundary condition. Such a model can be solved in the Vertex-IRF framework with arbitrary gauge parameters: we can diagonalise the transfer matrix by means of generalised Sklyanin's Separation of Variable (SoV) approach in a family of SoV bases that depend on two arbitrary gauge parameters $\alpha$ and $\beta$, $\beta$ being the so-called dynamical parameter and $\alpha$ an arbitrary shift of the spectral parameter. We show here that such SoV bases depend actually on $\alpha$ and $\beta$ through the difference $\alpha-\beta$ only. Considering the ungauged limit in which $\alpha-\beta$ tends to infinity, we show how to compute all elementary building blocks for the correlation functions of this model. We finally show how to compute overlaps between eigenstates of this model and eigenstates of a spin chain sharing the same boundary condition at site $N$ and in which the gauge invariant boundary condition at site 1 has been changed to a more general one.

Superconducting cosmic strings (SCSs) are characterized by three parameters: the dimensionless string tension $G\mu$, the current amplitude $Y$, and the vector coupling, $\tilde{e}$ as recently explored in \cite{Rybak:2024our}. Using the Charge-Velocity-dependent One-Scale (CVOS) model, we compute the stochastic gravitational wave background (SGWB) emitted by current-carrying loops, including the suppression effect of vector radiation. While previous studies have shown that large $\tilde{e}$ suppresses the SGWB, allowing larger $G\mu$ to evade pulsar timing array (PTA) bounds \cite{Rybak:2024our}, we demonstrate that this parameter space is definitively constrained by an independent, astrophysically clean probe: the Dark Ages global $21$-cm signal. We recalculated the recently derived $21$-cm bounds \cite{Si:2025vsj} into the generic $(\tilde{e},Y,G\mu)$ parameter space and find that at the threshold where vector radiation emission starts dominating, any coupling $\tilde{e}\gtrsim 10^{-7}$ and $Y\simeq 0.67$ and $G\mu\gtrsim 10^{-13}$ injects sufficient ionizing radiation to completely erase the $21$-cm absorption signal at redshift $z\simeq89$. Greater current amplitudes impose more stringent constraints. This excludes a large parameter space considered viable. Our model-independent results highlight the complementarity between future lunar-based $21$-cm experiments and gravitational wave (GW) observatories.

We propose a thermodynamic description of the genuine Kerr-Bertotti-Robinson (Kerr-BR) black hole spacetimes. Contrary to previous studies, such solutions no longer have electric charge. Consequently, the thermodynamics is governed by simple relations. Namely, upon introducing a suitable normalization factor for the timelike Killing vector, these spacetimes are characterized by the standard Hawking temperature, Bekenstein's entropy, Komar mass and angular momentum, and horizon angular velocity. The corresponding mass is shown to obey the standard Christodoulou-Ruffini formula, along with the standard first law and Smarr relations. In fact, by a proper rescaling of coordinates and solution parameters, and up to a non-trivial parameter space constraint, we formally recover the thermodynamic quantities of the vacuum Kerr solution. This is used to bring the genuine Kerr-BR spacetime into a Kerr-like form.

We discuss the origin of the modes appearing at the Schwarzschild black hole horizon and decaying at integer multiples of the surface gravity. We argue that no excitations generated at the horizon by the plunging of a particle into a black hole can leave it. Our argument is based on the fact that, when the particle approaches the horizon, its speed is necessarily boosted to ultra-relativistic values and its near-horizon gravitational field becomes a Dray-'t Hooft shockwave, which is an exact, nonanalytic, and nonperturbative solution of Einstein's equations. The corresponding metric perturbations are localized at the horizon and can never reach a distant observer.

In a complete quantum theory, one would construct it based on what we can observe in a system and operationally define in our universe. This philosophy goes back to some of the original ideals of quantum theory defined by W. Heisenberg, N. Bohr, and others as part of the Copenhagen school of thought. We argue in this letter that that if one wishes to construct a complete quantum field theory, that it is most natural to construct it based on a nonlocal theory of observable principles. If this interpretation is valid, then the one-particle nonrelativistic limit that recovers quantum mechanics would as well be dynamically nonlocal. In this interpretation we derive the nonlocal Schrödinger equation. We will as well demonstrate that the canonical position–momentum commutator and the Heisenberg uncertainty principle emerge from translation covariance.

We present a holographic model of SU(3) color superconductivity (CSC) where a global color symmetry is spontaneously broken by a diquark condensate at finite baryon chemical potential. At $\mu_b=0$, a systematic stability analysis over all SU(3) channels recovers the known SU(2) s+p competition. Based on that, the finite $\mu_b$ further generalizes the s-wave order to an S1+iS2 structure. We find that $\mu_b$ enhances the critical temperature of the S1+iS2 phase while suppressing the p-wave – the latter vanishes beyond a certain $\mu_b$ when backreaction is included. This opposite trend reshapes the phase diagram: with increasing $\mu_b$, the balanced S+ phase (S1=S2) takes over the entire color-superconducting region. Our non-Abelian framework provides a concrete holographic description of global SU(3) symmetry breaking, relevant for understanding color-superconducting phases in dense QCD and may offer new insights into the physics of neutron-star interiors.

We study the inverse adjoint problem for a perturbative bosonic outgoing map. Within the polynomial bosonic canonical-commutation-relation (CCR) algebra, we prove a constructive integrability theorem: order-by-order preservation of the CCRs is sufficient to reconstruct recursively a formal self-adjoint generator whose exponential implements the outgoing map by adjoint conjugation. At each order, the Baker–Campbell–Hausdorff contribution determined by previously reconstructed generators is subtracted from the outgoing coefficient, and the remaining homogeneous CCR conditions determine the next generator explicitly. We apply the construction to graviton scattering in the null-surface formulation (NSF), specialized to the flat solution-space sector with Minkowski metric, null generators, affine parameter, and cone measure. The NSF outgoing map preserves the Ashtekar radiative CCRs through (\delta a_3), corresponding to order (\varepsilon^2). At this order, the scalar CCR sector uniquely selects the symmetric ordering (c=1) for the nontrivial interacting kernel. The associated linear contraction, generated by the same cubic kernel, cancels the double-contraction contribution from ([\delta a_2,\delta a_2^\dagger]). The theorem then reconstructs the self-adjoint generators (\delta T_1) and (\delta T_2), providing a formal perturbative unitary implementation. The resulting canonical organization also separates the direct (2\to2) contribution into irreducible-loop, one-particle-reducible, and factorized sectors.

We formulate a data-completeness test for extracting low-energy characteristic-cone running from flat-space on-shell renormalization-group residues. In four-dimensional, parity-even Einstein–scalar–Maxwell effective field theory through four derivatives and four external fields, Wilson directions are first placed on the physical EFT quotient and background propagation is represented by a traceless response on the full massless root sector. The response is identifiable from chosen amplitude coordinates precisely when the amplitude kernel lies in the response kernel. For the published opposite-helicity vector–scalar residue we find $\beta_\mu C_{\gamma\phi}^{(2)}=-55/(96\pi^2)$ and, after an order-reduced frame translation, the contribution $\beta_\mu(r_T-r_\gamma)=-55/(48\pi^2M_{\rm P}^4)$. A finite operator registry gives explicit rank-two incompleteness tests: independent $F^4$ directions split photon polarizations on a magnetic background, while $\mathcal CFF$ produces an analytic splitting along a principal Weyl axis on a Petrov-I Einstein–scalar background. For the isolated scalar–photon contact, direct Schur reduction finds nonzero raw mixing but no first-order physical off-diagonal entry, by the Maxwell Ward identity. Thus the residue fixes one diagonal cone contribution but does not determine the term-complete characteristic response over the declared admissible coefficient domain.

We utilize the standard T-duality procedure to derive the classical effective action of heterotic string theory at the eight-derivative order within the NS-NS sector, which comprises the metric, the \(B\)-field, and the dilaton. Starting from the minimal basis at this order, consisting of 872 even-parity and 477 odd-parity couplings, we perform a dimensional reduction on a circle and impose invariance under T-duality transformations, specifically the Buscher rules supplemented by higher-derivative corrections. This invariance uniquely fixes a subset of the couplings to match those of type II theory up to an overall factor, while the remaining couplings are determined in terms of the coefficients at order \(\alpha'\). For these latter couplings, we adopt both the Metsaev-Tseytlin and Meissner schemes. Subsequently, through field redefinitions, we recast the action into a canonical form in which the dilaton appears solely through the overall factor \(e^{-2\Phi}\). In the Meissner scheme, the pure gravity sector precisely reproduces the known S-matrix results. In both schemes, the pure gravity terms can be expressed as the double trace \((\Tr(R^2))^2\), and when combined with the corresponding Yang-Mills terms \((\Tr(F^2))^2\), they take the unified form \((\Tr(R^2-F^2))^2\), as anticipated in the literature.

A black hole need not ring down in isolation, since a nearby companion can subject it to an external gravitational tide. We calculate how a quadrupole tide modifies the Schwarzschild black hole resonances. Linearising the exact tidally distorted Schwarzschild solution in the tidal amplitude $A$, we derive the diagonal odd- and even-parity perturbation equations on the deformed background and compute the formal first order displacements of analytically continued Schwarzschild resonances. Each diagonal first order shift factorises as $\delta\omega_{n\ell m}=A\,c_{\ell m}\kappa_{n\ell}$, giving one reduced complex coefficient for each $(n,\ell)$, expressed as a ratio of contour integrals, multiplied by a universal Zeeman-like pattern that splits the $2\ell+1$ azimuthal multiplet. For the $\ell=2$ and $\ell=3$ sectors analysed explicitly, the odd- and even-parity shifts coincide, so Schwarzschild isospectrality survives at first order in the tidal amplitude. Quadratic tidal forces, by contrast, can break this degeneracy. Moreover, for a physical companion, the astrophysically dominant $(n,\ell,m)=(0,2,2)$ mode oscillates faster and decays more slowly. Finally, we show that the eikonal shifts admit a geometric description in terms of the Penrose limit about the tidally deformed photon ring.

We investigate the flavor structures of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) subject to non-invertible selection rules. In particular, we classify the flavor textures of all baryon-number-conserving dimension-six SMEFT operators and determine the resulting constraints on their Wilson coefficients. The selection rules determine not only the texture zeros but also the allowed tensor structures of the Wilson coefficients, which can be expressed analytically in terms of a reduced number of independent parameters. We also find that the flavor structures of higher-dimensional operators are not necessarily aligned with those of the Yukawa couplings, in contrast to the Minimal Flavor Violation hypothesis, in which the Yukawa couplings govern the flavor structure of higher-dimensional operators. It turns out that the resulting flavor and chirality patterns differ from those typically obtained in SMEFT with conventional flavor symmetries, providing characteristic predictions for $B$-meson observables and charged-lepton-flavor-violating radiative decays.

Fractional Laplacians encode anomalous scaling and covariant nonlocal response in quantum matter and holographic boundary systems. We place the corresponding scalar spectral theory on a dynamical closed worldsheet. A metric-dependent intertwiner maps the fractional quadratic form to that of $D$ free bosons, while its zeta Jacobian changes the matter determinant weight from $D$ to $sD$. The prime-determinant transformation includes the zero-mode area factor and determines both the moduli density and the Weyl coefficient $c_{\rm det}=sD$. Weyl cancellation therefore selects $D_\ast=26/s$. On the integer critical locus $1\leq D\leq26$, $N=26-D$ spectator bosons turn the residual determinant into a local critical CFT. Its fixed-area genus-$g$ vacuum measure is that of 26 free bosons, its torus trace is modular invariant, its plumbing channels are state resolved, and its BRST charge is nilpotent. The $D$ distinguished coordinates remain spectral composites; their pullback yields the Koba–Nielsen amplitudes and massless vertex conditions. Target backgrounds coupled to this distinguished sector retain the ordinary one-loop tensor beta functions, with dilaton deficit $sD-26$ and the corresponding string-frame action. Worldsheet gravity thus turns the fractional exponent into a quantum-geometric consistency parameter.

We provide a perspective into measuring the quantum information spreading by introducing N-operator correlators. Leveraging the idea from N-point correlation function from cosmology, we formulate a generalized Out-of-Time-Ordered Correlator (OTOC), called N-Operator Correlator (NOC). Such formulation can reduce the effect of restricted analysis associated with selecting only two operators for OTOC. NOC can take into account a larger set of measurement probes in measuring the degree of quantum information spreading. We demonstrate these concepts with two analytically tractable toy systems with computing thermal averages of operator time evolutions at a finite temperature: a single qubit in longitudinal field and XYZ two-qubit system. Our perspective serves as a basic introduction to generalized operator correlators in quantum mechanics.

Within the open quantum system formalism, using the Markovian process, we investigate the quantum speed limit time (QSLT) of a uniformly accelerated Unruh-DeWitt detector, interacting with the massless real scaler field. Three specific scenarios are being studied – the field is in Minkowski spacetime (i) without any reflecting boundary but at a finite temperature, (ii) presence of single boundary with the detector is accelerating parallel to the plane of it, and (iii) presence of two boundaries with the detector is moving between them along the parallel direction. Interestingly, the behavior of QSLT appears to be very distinctive around a particular value of $a$. For the first scenario QSLT shows very noticeable change around a specific $a$ and the required value of $a$ corresponding to this change decreases with the increase of field temperature. In the other two scenarios, QSLT starts to fluctuate after a critical value of $a$. If we further increase $a$, more vigorous fluctuation emerges. The value of $a$ required for the starting of the oscillation is much less for the double boundary case compared to the single boundary. Taking into account specific values of the distance between the boundaries and the detector's frequency, we estimate that the critical value of $a$ can be as low as $\sim 10^5 \text{m}/\text{s}^2$ for the double boundary situation. We argue that such a distinctive feature in QSLT can be a fruitful tool to diagnose the Unruh effect.

We present a spacetime that describes a rotating and charged black hole immersed in an external magnetic field. This exact solution to the Einstein-Maxwell equations has a surprisingly simple form which reduces to standard Kerr-Newman metric, and to the uniform Bertotti-Robinson magnetic universe. We show that the Kerr-BR solution presented in [Phys. Rev. Lett. 135, 181401 (2025)] has a special charge, and we identify a genuine Kerr black hole without any charge, in the magnetic field. In the weak-field limit it gives the Wald solution. We analyze main physical properties of the new family, namely singularities, horizons, regularity of axes, charges, entropy and temperature.

We study the radiative correction to the mass of the $(1+1)$-dimensional $\lambda\phi^4$ kink in the presence of an irreducible, spacelike Lorentz-violating interaction. The Lorentz-violating operator is chosen as $-\frac12 c\phi^2(u\!\cdot\!\partial\phi)^2$ with $u^\mu=(0,1)$, which is the lowest-order single-scalar operator considered in this class of models that produces effects that cannot be removed by a linear redefinition of coordinates or the field. We perform the one-loop renormalization of the underlying quantum field theory. In contrast with Lorentz-invariant $\lambda\phi^4$ theory in two dimensions, the Lorentz-violating theory requires, at this order, both a modified mass counterterm and a nonzero field-strength counterterm. The corrected stability problem contains modified bound and continuum modes, while the continuum phase shift remains unchanged at $O(c)$ with the boundary-condition prescription adopted here. Finally, using the vacuum-subtracted zero-point energy and the counterterm Hamiltonian, we obtain the one-loop kink mass through first order in $c$. We give the finite coefficient in the subtraction prescription implemented in the accompanying thesis calculation, for which the Lorentz-violating contribution is numerically negative.

Recently we have demonstrated that black hole radiation can be smoothly extended to the zero-temperature limit. Here we analyse entropy variations at the zero temperature limit and evaluate the validity of the Generalized Second Law (GSL). Typically one verifies that the entropy gain in the exterior region compensates for the entropy loss of the black hole due to evaporation. However an anomalous feature emerges at the zero temperature limit. The fact that the emission is restricted to the modes $\omega <m\Omega$, renders the variation of the horizon area of a Kerr black hole positive definite. Simultaneously the von Neumann entropy of the exterior region increases both for bosonic and fermionic modes. The dual entropy gain at the zero temperature limit marks a robust conservation of the GSL. We demonstrate that the dual increase also applies to Kerr-Taub-NUT black holes whose entropy is neither directly proportional to the horizon area nor analytically integrable.

Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N < \infty$. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite $N$, both in QM and in QFT.

We prove that black-hole isospectrality between linearly independent solutions follows whenever radiative metric and matter perturbations are reconstructed from complex master variables obeying a closed, complex-linear system with complex-linear boundary conditions. If a phase rotation maps one parity sector to the other, then the even- and odd-parity QNM spectra coincide, and the perturbations are parity isospectral. A broad class of chiral-aligned theories satisfies these criteria. As an application, we demonstrate that subextremal Kerr–de Sitter black holes are parity isospectral.

One aim of neural network field theory is to put a quantum or effective field theory on a computer, with the network ensemble itself as the theory. We ask how far that aim can be pushed for a function class regular enough to be computed with. Our main result is a no-go theorem with assumptions that hold for standard network architectures. We use it to separate four versions of neural network field theory, according to whether the defining object is the finite width ensemble or its infinite width limit, and whether the target we want to compute is a quantum or an effective field theory. Neither finite width interpretation is straightforwardly consistent. For finite width ensembles with finite variance at each point, the QFT interpretation fails reflection positivity, while the EFT interpretation establishes no scale separation by which the positivity violation can be placed outside its domain of validity. Of the two limit versions, one can be simulated in full and the other only in part, as only its smeared correlators are computable with a controlled error. As such, at the level of a controlled numerical computation, the QFT and EFT versions cannot be distinguished. One dimension escapes the obstruction, yet reflection positivity is shown to still fail there at every finite width for the cosine network. Two escapes from the theorem remain, giving up either finite variance at a point or exact rotation invariance, and we discuss both of these possibilities.

With a view towards understanding flat space holography, we study the flat space limit of asymptotically $AdS_4$ black holes in gauged $\mathcal{N}=2$ supergravity. Using holographic renormalisation, we carefully analyse the flat space limit of the on-shell action of various black holes in this setting and make explicit the states that contribute to the partition function in this limit. We find several features: large black holes lead to a divergence in the partition function which can be understood as a thermodynamic volume divergence. Meanwhile, semiclassically, small black holes reproduce the partition function of their flat space counterparts, and we clarify the mapping between BPS, (near-)extremal or non-extremal black holes on both sides for charged and rotating solutions. Finally, by studying a suitable flat limit of the BPS Kerr-Newman-$AdS_4$ black hole in M-theory, we obtain a charged BPS solution in flat space. On the dual side, we determine a Carrollian-like limit on the known ABJM partition function on $S^1\times S^2$ at large $N$, and show that it reproduces the correct entropy of the BPS charged black hole in asymptotically flat space.

We discuss aspects of the black hole-string transition as the angular velocity approaches the supersymmetric index $\beta \Omega = 2\pi i$. In this limit, the high-temperature Atick-Witten effective description breaks down. For Heterotic string theory, a new high-temperature description emerges near the index in terms of a Higgsed $SU(2)_L\times U(1)_R$ supergravity with a magnetic field profile. The Hagedorn instability manifests in the theory as Ambjorn-Olesen W boson condensation, due to the background magnetic field. For type II, a tower of winding strings becomes light near the index, which opens up a new dimension in the T-dual picture. In both cases, a string star solution is found, similar to the Horowitz-Polchinski solution, but decouples at the index $\beta \Omega = 2\pi i$. Considering charged solutions, the string star appears to interpolate between charged black holes and the free string phase. At the index, both the charged black hole and the charged string star phases decouple. This suggests a tension between a smooth black hole-string transition and the existence of a stringy BPS two-charge black hole.

We develop a formalism for extracting relativistic classical dynamics from the S-matrix, in which massive bodies are described on phase space while massless radiation is kept in the Fock space. Our formalism relies on the Stratonovich-Weyl (SW) correspondence between the operator and phase-space formulations of quantum mechanics, as implemented covariantly by the SW quantizer. For localized incoming states, classical observables are given by SW symbols of the appropriate operators evaluated on incoming asymptotic trajectories. In combination with the exponential form of the S-matrix, the observables are naturally given by nested mixed Dirac/commutator brackets involving Magnus amplitudes. The latter are the matrix elements of the logarithm of the S-matrix, and we provide a straightforward algorithm for computing the combinatorial Murua coefficients that control the placement of retarded propagators inside Magnus-amplitude diagrams. This picture is well-suited for gravitational-wave physics applications.

We develop a phase-space description of classical scattering in which the matter sector of the Dyson S-matrix is partially Weyl transformed while the radiation sector remains operator valued. The resulting S-matrix symbol provides a common origin for several classical observables: we show that the inclusive waveform, the classical displacement in phase-space (i.e. the impulse and position shift), and the angular momentum arise as different projections of the same object. We show that the partially Weyl-transformed $S$-matrix admits an exponential organisation in terms of an elastic phase and connected radiation kernels, while its inclusive one-point projection admits a coherent representative with waveshape $\alpha_I$ describing classical radiation, extending our recent proposal. Furthermore, we show explicitly how nonlinear gravitational memory can be derived from an inclusive coherent waveshape. The dependence of the waveshape on the hard scattering data naturally leads to a quantum geometry, including an induced Berry connection on the space of waveforms, whose contribution to the phase-space displacement captures both radiation-reaction and static-field effects. We illustrate this structure by deriving static contributions to the position shift and field angular momentum in both scalar QED and gravity.

Previously, it was shown that the interplay between the gravitational memory effect and the thermodynamics of an ensemble of spinning objects gives rise to a hysteresis effect, which can be termed Gravo-Thermo memory. This effect can be studied either through a statistical approach or via kinetic theory. Here, we present a general kinetic theory model for the general case of a fluid composed of spinning extended objects in the presence of gravity.

Inspired by quantum field-theoretic constructions of 4d $\mathcal{N}=1$ quiver gauge theories that flow to superconformal field theories (SCFTs), we construct 7d manifolds of $G_2$-holonomy, which geometrically engineer these quivers in M-theory. Field theoretically, the 4d quivers are obtained by flux torus compactifications of 6d $\mathcal{N}=(1,0)$ SCFTs. The 6d theory compactified on a circle gives rise to a 5d KK-theory, which has a geometric realization as M-theory on a non-compact elliptically fibered Calabi-Yau threefold. Following the field-theoretical prescription, these local geometries are fibered over a circle to realize (topological) $G_2$-holonomy manifolds. We carry this out concretely in the case of the rank 1 E-string theory and its 4d quivers and construct new families of $G_2$-holonomy spaces.

We represent sandwiched and $\alpha$-$z$ Rényi divergences as averages of ordinary relative entropy. The $\alpha$-$z$ Rényi divergence is shown to be an integral over the relative entropy of a canonical family of fixed-ray escort states along the ray $z=c\alpha$. We prove this representation for normal states on an arbitrary von Neumann algebra, using Haagerup non-commutative $L^p$ spaces and interpolation. The formula holds for every $z>0$: for $0<\alpha<1$ it holds when the support of the first state is contained in that of the reference state, and for $\alpha>1$ it holds whenever the divergence is finite. When the lower-order support condition fails, we identify the exact fixed-ray support-boundary term. The representation yields a monotone escort profile and a convex order potential. We use these to reformulate one-shot testing converses, exact sandwiched strong-converse exponents, and work-extraction reliability as signed-area or level-crossing statements, and discuss a restricted two-parameter pair-conversion rate.

In a recent paper \cite{Chu:2026dhx}, the quantum stability of the fuzzy sphere was established at large but finite $N$, where a tadpole was also identified for the scaling fluctuation mode of the matrix geometry. Here we show that this tadpole generates a positive area-conjugate microscopic response, which in isolation energetically favors contraction of the fuzzy sphere. However, when the horizon is coupled to gravity, the tadpole requires the bulk geometry to adjust according to the junction condition of general relativity. Taking the exterior geometry to be Schwarzschild, we show that the junction condition requires a positive interior cosmological constant. Imposing a static, spherically symmetric, regular vacuum interior then selects pure de Sitter space. The matching further determines a soldering relation between the interior de Sitter time and the exterior Schwarzschild time, with a relative lapse growing as $C = O(N)$. We also propose a matrix realization of the de Sitter interior in which fuzzy-sphere representation sizes determine the angular geometry while condensates of off-diagonal link fields determine the emergent radial metric. This provides a concrete consistency test for spacetime emergence from the matrix degrees of freedom. Potential cosmological implications are discussed.

There are five independent four-derivative superinvariants for the five-dimensional STU model, of which two are vector invariants that do not involve curvature tensors. We construct the corrected BMPV black hole directly in five dimensions with this set of general four-derivative couplings, a computation made possible with the help of AI. We find that the vector invariants do not correct the solution or the entropy, while the entropy associated with the heterotic corrections agrees with recent results.

Classical fusion of sigma-model defects is commonly approached by combining their worldsheet actions and eliminating the intermediate fields. This procedure, however, does not systematically identify the resulting target-space defect or its possible branches. We address this problem by formulating fusion as a reduction of the target-space defect data. Local descent of the intrinsic two-form and global descent of the connection determine the admissible branches. For symmetry-preserving bi-branes in the $SU(2)$ WZW model and Hopf-fibre T-duality defects, the prescription reproduces the known biconjugacy-class branches and the finite family of fibre-shift defects. The appearance of several branches provides a classical manifestation of non-invertible fusion. We further use the framework to construct TsT and T-dual biconjugacy defects, including their global consistency conditions. It therefore provides a systematic method for computing classical fusion and constructing new defects from known ones.