Papers

We suggest a non-minimal renormalization scheme based on dimensional regularization that naturally incorporates threshold effects of heavy particles. By renormalizing couplings and masses to subtract all poles in $d \geq 4$, the resulting scheme is mass-dependent and circumvents shortcomings of mass-independent schemes like minimal subtraction. At the same time, many advantages of minimal subtraction such as gauge independence are retained. Through explicit one-loop computations in QCD, we demonstrate that this scheme reduces to minimal subtraction at high energies while providing smooth transitions at particle thresholds and implementing the Appelquist-Carazzone theorem. Potential future applications and extensions are discussed.

Recent developments of Batalin-Vilkovisky (BV) formalism and related geometry are reviewed. Mathematical structures of BV formalism are summarized as a Q-manifold and a QP-manifold. Lie algebras, Lie algebroids and other higher algebroids are explained as typical examples of Q- and QP-manifolds. Finally, the BV action functionals are constructed by geometric structures of Lie algebroids and Courant algebroids.

The invariant mass spectrum of $e^+e^-$ pairs produced in high-energy Pb-emulsion collisions at 160 A GeV at CERN SPS exhibits a highly complex structure of a broad enhancement at 11$\pm$1 MeV with a full width of about 10 MeV, and additional many narrow resonances within the experimental bin width of 2 MeV, including a prominent narrow resonance at 19 $\pm$1 MeV that provides an independent support for the hypothetical X17 particle. We show that the highly complex spectrum may be coherently described as the signatures for the neutral color-singlet $q\bar q$ quark matter in both its deconfined phase as well as its confined phase. That is, the broad enhancement at 11$\pm$1 MeV may arise from thermal annihilation of QED(U(1))-deconfined quarks and antiquarks into $e^+e^-$ pairs at the phase transition temperature $T_c$(QED), which can be theoretically estimated to be 4.75 $\pm$ 1.04 MeV from the transitional equilibrium condition. The observed narrow resonances at 3$\pm$1 and 7$\pm$1 MeV may correspond to the QED(U(1))-deconfined $u\bar u$ and $d\bar d$ Coulomb bound states near their quark rest masses, respectively, whereas the observed narrow resonance at 19 $\pm$ 1 MeV may correspond to the QED(U(1))-confined isoscalar QED meson. The approximate agreement between the theoretical and the experimental spectrum suggests tentatively that both QED(U(1))-confined and QED(U(1))-deconfined neutral color-singlet $q\bar q$ quark matter may have been produced in these high-energy Pb-emulsion collision, pending confirmation of the Pb-emulsion collision data. We propose future experiments to confirm or refute these findings.

We present an invariant characterization of the Kerr spacetime, and utilize the invariant structure of the spacetime to derive a function whose zeros identify a special family of null geodesics. Each member of this family is tangent to every photon surface in the Kerr photon region, offering a method of invariantly characterizing photon surfaces in axially symmetric spacetimes and thereby a providing a computational tool for efficiently computing the geodesic equations for any part of the photon region. The invariant that identifies all of the spherical photon orbits is parameterized by a Lorentz parameter, where the parameter is effectively an inclination angle of the spherical photon orbits through the equatorial plane. We also show how the invariant determines the constants of motion for all spherical orbits in the photon region. Finally, we briefly derive invariants which identify the other geometrically important surfaces such as the ergosurfaces and local horizons.

For supersymmetric extensions of the Standard Model we construct some expressions that include Yukawa couplings for the third and second generations and receive relatively small quantum corrections. This implies that they slightly depend on scale and are therefore approximate renormalization group invariants. Using these invariants we try to analyse possible relations between the Yukawa couplings at the unification scale $M_X$ for some values of $\mbox{tg}\,\beta$ for the MSSM and its extensions containing certain additional superfields forming complete $SU(5)$ multiplets.

We expect black hole microstates to differ in their chaotic properties from states associated with other geometries. For supersymmetric black holes, ordinary level statistics cannot diagnose this distinction, since their energy levels are exactly degenerate. We propose that there is an intrinsic probe of chaos, encoded in the mixing of the microstates under changes in the couplings of the theory, as determined by the non-Abelian Berry curvature of the BPS states under certain deformations. For states dual to horizonless geometries in holographic systems, such as 1/2-BPS states in the D1/D5 CFT and 1/4-BPS states in $\mathcal{N}=4$ SYM, we find that the Berry curvature for marginal deformations is non-random and often exactly zero at generic couplings. By contrast, for states dual to supersymmetric black holes, we show through computations in $\mathcal{N}=2$ super-JT gravity and explicit numerics in the $\mathcal{N}=2$ SYK model that the Berry curvature resembles a random matrix. We also uncover interesting topological features of the $\mathcal{N}=2$ SYK moduli space, as probed by Chern numbers. These results suggest that the Berry curvature sharply distinguishes black hole microstates from smooth horizonless states and provides a robust diagnostic of chaos in supersymmetric sectors.

We investigate formulations of quantum field theories whose kinetic terms involve fractional or continuous powers of the d'Alembert operator. The primary requirements are perturbative unitarity and a well-defined classical limit with a finite number of initial conditions. A direct approach consists of continuing the correlation functions from Euclidean space to Minkowski spacetime using the fakeon prescription for the fractional part of the power. Alternative formulations arise through decomposition, in which the fractional part is represented as a continuum of ordinary fakeons. These options are infinite in number and yield inequivalent Minkowskian theories with the same Euclidean counterpart. We demonstrate these features at tree level and for bubble diagrams. We also point out potential pitfalls in the calculations. Finally, we show how to treat continuous powers of covariant d'Alembertians in fractional gauge and gravity theories. The Ward and Cutkosky identities hold in all formulations.

We construct an effective light-front mass-squared operator for quark-antiquark systems that incorporates quark dressing effects through a running quark mass. Starting from a Minkowski-space quark propagator constrained by lattice-QCD-inspired parametrization, we derive the disconnected light-front resolvent for a light quark-antiquark system using a generalized spectral representation of an individual quark propagator separating out the instantaneous contributions. By projecting the resolvent onto a constituent-quark helicity basis, we obtain an effective dressed mass-squared operator suitable for light-front Hamiltonian approaches. We introduce an effective light-front quark self-energy and analyze its momentum dependence. As an application, we study pion structure using representative light-front wave-function models and compute unpolarized transverse-momentum-dependent distributions, unpolarized parton distribution functions and distribution amplitudes. Our results show that quark dressing induces sizable infrared modifications while preserving controlled ultraviolet behavior, providing a framework to incorporate nonperturbative QCD dynamics into light-front descriptions of hadrons.

In this work we analyze the classical confinement of relativistic and supersymmetric spinning particles in higher-codimension braneworlds. Considering warped backgrounds generated by string-like $ n=2$ and global scalar defects $ n \geq 3$, we derive the effective radial dynamics from a Polyakov-type action. For spinless particles, the effective potential is monotonically decreasing, leading to repulsive behavior and the absence of confinement. In contrast, for $N=1,2 $ spinning particles, spin-curvature coupling modifies the potential, allowing the emergence of stable equilibrium points. Depending on the coupling parameter, particles may be confined on the membrane or in nearby regions, exhibiting bounded or satellite-like motion. These results emphasize the role of spin in localization mechanisms.

We extend kinematic flow to a class of momentum-integrated loop-level cosmological correlators: banana loops of conformally coupled scalars in power-law cosmologies and, in de Sitter, banana loops containing arbitrary mixtures of massless and conformally coupled scalars. Exploiting their dual description as tree-level exchanges of unparticles, we show that the associated correlators are described by a finite set of master integrals obeying a first-order system of differential equations. The corresponding basis is constructed from tubings of marked graphs and is distinguished by the appearance of nested tubes and an arborescence ordering of the vertices. We derive the connection matrices from four combinatorial rules—activation, merger, swap, and copy. The last two are unique to unparticle exchanges: they induce richer mixing among basis functions and introduce new kinematic letters. Our framework extends systematically to arbitrarily complicated configurations, including necklace diagrams, and establishes unparticle exchange as a distinct class of kinematic flow.

I briefly summarize a recent research program aiming to probe the landscape of low-energy phases of string theory from a global perspective. Borrowing conceptual lessons from the swampland program, I will discuss how the effective theories of gravity produced by low-energy string theory are far from generic; rather, their infrared data is connected by universal scaling relations which become non-trivial in species limits. In particular, a worldsheet analysis reveals that higher-derivative Wilson coefficients and the vacuum energy exhibit UV/IR relations which are invisible from the viewpoint of effective field theory, leading to parametric inequalities which take the form of holographic bounds. This lends a more solid theoretical support to swampland-motivated phenomenological scenarios, and to the broader hopes of extracting less direct, but empirically accessible, signatures of string theory from cosmological observations.

M-theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ has recently been proposed to yield, via quotients, ten-dimensional non-supersymmetric string theories. We revisit the construction that leads to the heterotic theories, finding a consistent set of rules that reproduces the light spectra and gauge groups, including indications of their global structure. Our approach uses the gauge enhancement mechanism of type I' string theory, applied to a setting in which the type I' interval is curled onto itself, with its two boundaries separated by a branch cut. Using these tools, we reproduce the ten-dimensional heterotic theories and provide some evidence for junctions among them.

We study free Carrollian quantum field theories from an algebraic perspective and explore their implications for flat space holography. As explicit examples, we construct the electric and magnetic Carrollian Weyl algebras obtained from Carroll limits of the relativistic scalar field and analyze their states, including vacuum and thermal configurations. For the massive electric theory, we find a regular Carroll-invariant vacuum state and a regular KMS state, yielding a consistent Carrollian thermodynamic system. By contrast, the massless electric and magnetic theories are more subtle: depending on the quantization, they admit either no regular distinguished vacuum or only nonregular Carroll-invariant ground states, while still supporting nonregular thermal states. We further analyze alternative classes of states in the massless electric theory, including spatially homogeneous quasifree pure states and Sorkin–Johnston states. Motivated by these results, we discuss consequences for flat space holography. We construct a well-defined state relevant for Carrollian holography whose Hilbert-space representation factorizes into a standard Fock sector and a nonseparable zero-mode sector, thereby highlighting the role of infrared degrees of freedom in the boundary theory.

Since their rediscovery in the 1990s, multiple zeta values have become ubiquitous in many areas of mathematics and physics. Their standard integral and sum representations can usually be traced back to a single source, namely the iterated integrals on the Riemann sphere with three punctures. We refer to such representations as the linear geometry of multiple zeta values, since the denominators of the corresponding integrands factor completely into linear terms. However, there also exist equally important and entirely distinct integral representations for multiple zeta values arising in mathematics and physics, in which matrix determinants appear in the denominator of the integrand. We call this the non-linear geometry of multiple zeta values. These lectures trace the origins of this non-linear geometry and provide an introductory journey through a range of topics including tropical geometry, the moduli spaces of tropical curves, Feynman integrals in quantum field theory, the general linear group of integer matrices, and the reduction theory of quadratic forms. In doing so, we propose a geometric framework for multiple zeta values based on such non-linear, determinantal representations and set out a number of open questions for future research.

We investigate the scalar sector of linear cosmological perturbations in quadratic gravity. Working in the Einstein frame, we derive the equations of motion in a gauge-independent manner and express them in terms of three sets of gauge-invariant variables. This approach allows us to distinguish genuine physical effects from gauge artefacts, which is particularly relevant for assessing the stability of perturbations in this theory. In the superhorizon limit, we obtain the leading-order behaviour of the relevant gauge-invariant variables and analyse the perturbations in commonly used gauges. We find that the Newtonian gauge exhibits an apparent instability, characterised by the exponential growth of the metric perturbations. However, this growth is non-generic and gauge-dependent; in the other gauges analysed in this work, the perturbations remain well behaved within the perturbative regime. Our analysis also demonstrates how the evolution behaviour of a gauge-invariant variable changes under the frame transformation and clarifies the relation between results obtained in the Jordan and Einstein frames.

We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point amplitude or equivalently the normalized quadrangular Wilson loop with a Lagrangian insertion. By analyzing the relevant Landau diagrams recursively, we prove that this quantity has singularities only at $z=-1,0$ and $\infty$ to all loop orders. This represents a first step towards obtaining a non-perturbative resummation for this quantity at next-to-leading order in the expansion over cycles.

A nonzero neutrino magnetic moment arises already in the minimally extended Standard Model with right-handed massive Dirac neutrinos. The well-known consequence of the neutrino magnetic moment is the phenomenon of neutrino spin oscillations in a magnetic field. It can manifest itself not only as a lack in the flux of active cosmic neutrinos arriving on Earth but also as characteristic features in low-energy neutrino elastic scattering processes. Following our approach developed earlier, in this work we study the influence of arbitrary spin-flavor state of incoming neutrino on low-energy neutrino scattering off different particles in a detector. We demonstrate that superposition of left- and right-handed helicity neutrino states gives rise to an azimuthal asymmetry in the angular distribution of the recoil momenta. We present numerical calculations for elastic neutrino scattering on electrons, protons and 40Ar and 132Xe nuclei, demonstrating the azimuthal-asymmetry effect. Our results indicate the unique potential of directional neutrino detection to observe the neutrino spin oscillations.

Sati and Schreiber [arXiv:2402.18473, arXiv:2512.12431] have proposed that charge quantisation in quantum field theory and string theory is governed by a homotopy type $\mathcal A$. We provide a refinement of this postulate, incorporating other currents including matter, connecting it to adjustments in higher gauge theory and providing a prescription for determining $\mathcal A$, and show that, while the homotopy groups of $\mathcal A$ classify the possible brane charges, the homology groups of $\mathcal A$ classify the invertible higher-form symmetries. Furthermore, we show that the charge-quantisation postulate implies a number of non-trivial constraints on quantum field theories similar to those implied by swampland conjectures; in particular, it rules out noncompact gauge groups and one-form field strengths that form a non-nilpotent Lie algebra. Finally, we argue that for theories of quantum gravity the space $\mathcal A$ must be contractible, in accordance with the swampland conjectures on the absence of global generalised symmetries and the completeness of the spectrum of charges, and explain how this explicitly arises in the case of Type I string theory.

We use the framework of generalized entanglement wedges to revisit the connected wedge theorem (CWT). This construction identifies an entanglement wedge associated for any bulk region and allows us to rephrase the CWT in terms of the entanglement entropies of bulk regions. We establish new upper and lower bounds on the mutual information of boundary decision regions in terms of the entropies of certain bulk regions associated with a scattering configuration. We then define new bulk decision regions for which we show that a non-empty scattering configuration implies a connected entanglement wedge. This generalization of the CWT extends to asymptotically flat spacetimes.

A natural approach for constructing a concrete example of flat space holography is to take the flat space limit of a well-understood example of AdS/CFT, such as the one relating M-theory in AdS$_4$ times an orbifolded 7-sphere to a certain three dimensional superconformal Chern-Simons-matter theory known as the ABJM theory living in the boundary of AdS$_4$. In particular, taking the flat space limit of the bulk corresponds to taking the speed of light $c$ to zero in the boundary, giving rise to a Carrollian superconformal theory. This limit is subtle to implement for fermions, however, since the Dirac algebra is sensitive to the spacetime metric and therefore takes a different form in Carrollian spacetimes than it does in Minkowski space. In fact, we show that there are four possible ways of realising Carrollian fermions, one of which arises at leading order in the $c\rightarrow0$ limit of relativistic fermions. In three dimensions, there is an additional complication that the minimal realisation of the Carrollian Dirac algebra requires $4\times4$ matrices rather than $2\times 2$ matrices familiar from the relativistic case. Nevertheless, we show that the $c\rightarrow0$ limit of the ABJM theory can be recast in terms of Carrollian Dirac matrices and enjoys and infinite-dimensional Carrollian superconformal symmetry whose bosonic subsector is the extended BMS$_4$ algebra encoding the asymptotic symmetries of four dimensional Minkowski space. This provides a concrete starting point for constructing a Carrollian gauge theory dual to M-theory in flat space.

We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be converted into exactly gauge-invariant theory which under a suitable choice of gauge conditions can be treated within the formalism of minimal wave operators manageable by the covariant Schwinger-DeWitt technique. We carry out quantization of such a theory in general terms when the initial generators of gauge transformations are of the first and second stages of reducibility and derive its partition function in terms of the functional integral with all corresponding ghost fields. This method is applied to quantization of massive fermionic totally antisymmetric tensor field models in $AdS$ space. One-loop quantum effective action for these models is derived in the form of the functional determinants of special Dirac-type differential operators in various dimensions.

Black holes with resonant hair are static, spherical, electrically charged solutions of the Einstein-Maxwell-(gauged-)scalar system. Scalar self-interactions are mandatory for their existence. Initial dynamical studies restricted to spherical symmetry suggested stability; more recently, fully non-spherical dynamical studies revealed instabilities, at least for a particular class of self-interactions. Here, we provide a more detailed study of this instability together with a different decay channel, depending on the chosen solutions. Moreover, considering a second model, we provide evidence that the instabilities may be generic for different classes of self-interactions. We conclude these solutions are dynamically unstable and split into a bosonic lump and a bald black hole (via fission) or implode to the latter (via absorption). In both cases, the non-spherical dynamics seems to be key.

The Euclidean Kerr metric is conformal, in two distinct ways, to a Kahler metric, with conformal factors determined by the repeated eigenvalue of the two chiral halves of the Weyl curvature. A Lorentzian analogue holds, where the conformally related metric is complex but retains key features of Kahler geometry. We show that this hidden Kahler structure provides a geometric explanation for the existence of decoupled equations for curvature scalars, such as the Teukolsky equations. The essential mechanism is that, on a Kahler background, self-dual 2-forms are parallel with respect to a natural covariant derivative, so differential operators acting on them preserve their decomposition and do not mix components. In this way, decoupling is seen to be a direct consequence of Kahler geometry. We make this mechanism explicit in two ways. First, we show that the spin-k Teukolsky operator can be obtained from a Laplace-type operator associated with the Kahler metric by a similarity transformation. Second, for electromagnetic perturbations, we use the conformal invariance of Maxwell's equations delta F = 0 to show that they imply d delta F = 0, where delta is the co-differential of the Kahler metric. This operator automatically decouples, and the resulting equations for the extremal components coincide with the spin-one Teukolsky equations.

We develop a consistent mathematical framework for studying two flavor neutrino oscillations in presence of non-Hermitian dynamics. We consider two approaches : (a) bi-orthonormal inner product defined by a positive-definite metric operator $\mathcal{G}$ and (b) the density matrix prescription by Brody and Graefe [Phys. Rev. Lett. 109, 230405 (2012)]. For the $\mathcal{PT}$-symmetric case, we show that the $\mathcal{G}$ metric approach does not work well (probabilities are not conserved) both in $\mathcal{PT}$-unbroken as well as $\mathcal{PT}$-broken regime. Hence, we adopt the density matrix prescription by Brody and Graefe which is a positive semi-definite map. In the density matrix prescription, we note that probability in the steady state limit is not necessarily $1/2$ thereby indicating non-Markovian behavior.

We consider the ghost-free dRGT massive gravity with two of its three possible mass terms. This theory has five gravitational degrees of freedom. On Minkowski spacetime these modes have helicity-2, -1 and -0 and propagate on the Minkowski lightcone in the high-frequency limit. However for a general background the degrees of freedom corresponding to the helicity-1 and -0 modes have characteristics different to that of the metric lightcone. Here we prove in all generality, that the two degrees of freedom corresponding to the helicity-2 mode always propagate on the metric lightcone for any background in the high-frequency limit, which has significant relevance for current and future observational tests of the theory.

On $T^6/(Z_3 \times Z_3)$ heterotic orbifolds where three quark generations arise from $Z_3$ fixed-point triplication, we prove that the leading-order tree-level Yukawa amplitude – the three-point coupling among massless string states – has an exact column texture: $Y_{\rm lead}(i,j) = c\,\varepsilon^{q_R[j]}$, with the $O(1)$ coefficient $c$ universal across all left-handed generations $i$. Five independent lines of evidence are given: (1) the worldsheet instanton geometry on the $SU(3)$ root lattice gives identical areas for all non-degenerate triangles, making the geometric $O(1)$ coefficient exactly $1$; (2) the generation direction necessarily has trivial Wilson line, rendering all three generations gauge-identical, as verified across all 77 MSSM-like models in the Mini-Landscape classification; (3) an extension to two-Wilson-line models, verified on the complete Parr-Vaudrevange-Wimmer classification of 3,337 $Z_3 \times Z_3$ MSSM models, confirms that no Wilson line configuration can break gauge blindness; (4) the Kähler metric is generation-universal by $\Delta(54)$ representation theory; (5) the full Froggatt-Nielsen chain computation with 534 trilinear superpotential couplings and vacuum-aligned singlet VEVs produces left-circulant Yukawa matrices whose eigenstructure is generation-universal. The Froggatt-Nielsen column texture is therefore not an approximation but an exact property of the leading-order string amplitude. Non-trivial $O(1)$ coefficients, which are required for CKM mixing angles beyond the Wolfenstein hierarchy, must originate from beyond-leading-order contributions: integrated-out heavy messenger propagators (tree-level in the low-energy effective theory), vacuum-alignment effects, multi-instanton corrections, or loop corrections.

Within the framework of the one-boson-exchange model, we systematically investigate the interaction between the vector meson $K^{*}$ and the baryon $\Sigma^{*}$ with the aim of exploring the possibility of forming hadronic molecular states. The $K^{*}\Sigma^{*}$ interaction potential is constructed from $\rho$, $\omega$, and $\pi$ meson exchanges, and the nonrelativistic Schrödinger equation is solved using the Gaussian expansion method. The binding energies are calculated for different total angular momenta $J^{P}$ and isospin channels $I=1/2$ and $I=3/2$. Our results show that $S$–$D$ wave mixed $K^{*}\Sigma^{*}$ molecular states with $J^{P}=1/2^{-}$ can be formed only in the $I=3/2$ channel, while no bound state appears in the $I=1/2$ channel. In addition, the $S$–$D$ wave mixed states with $J^{P}=3/2^{-}$ and $J^{P}=5/2^{-}$ are also found to support bound-state solutions. For higher partial-wave states in our study, the binding mechanism mainly arises from the interplay between partial-wave mixing and non-central interactions. In particular, the $J^{P}=1/2^{+}$ channel does not support a bound state, as the meson-exchange interaction is predominantly repulsive. Our analysis further supports the interpretation of the experimentally observed $N(2250)$ and $\Delta(2200)$ states as $K^{*}\Sigma^{*}$ molecular candidates, corresponding to $I=1/2,\ J^{P}=9/2^{-}$ and $I=3/2,\ J^{P}=7/2^{-}$, respectively.

We construct an $SU(5)$ Grand Unified Theory on domain walls in the five-dimensional space-time. In this setup, we introduce an adjoint scalar field and a singlet that together form a set of five domain-wall solutions, realizing a dynamical brane-world. The same scalar fields also localize chiral fermion zero modes around the walls via the Jackiw-Rebbi mechanism, break $SU(5)$ down to the Standard Model gauge group via geometric Higgs mechanism and simultaneously trap gauge fields through a field-dependent gauge kinetic term. Furthermore, they enable localization of the Higgs field, providing a novel solution to the doublet-triplet splitting problem. As a result, all essential ingredients of the model are realized by a single adjoint scalar field and a singlet, making the construction very economical. We propose two realizations of the Higgs sector, derive the four-dimensional effective theory, and demonstrate that the Standard Model Yukawa couplings at the weak scale can be reproduced from the five-dimensional Yukawa couplings by the renormalization group analysis with a suitable choice of parameters.

We investigate the effective photon geometry associated with black holes in Kruglov nonlinear electrodynamics and its consequences for strong-field optical phenomena. This model constitutes a one-parameter generalization of Born-Infeld electrodynamics, interpolating between Maxwell theory and exponential electrodynamics through the parameter $q$. For a wide range of $q$, the spacetime geometry outside the event horizon remains close to the Reissner-Nordström solution, while photon propagation is governed by an effective geometry that depends sensitively on the nonlinear electrodynamics sector. We study the corresponding null geodesic structure through fully numerical calculations, focusing on photon spheres, light deflection, black hole shadows, and accretion-disk images. The effective geometry shows qualitatively distinct features depending on $q$. In particular, sufficiently small positive values of $q$ generate stable photon orbits outside the event horizon, together with significant modifications to the range of impact parameters supporting multiple photon trajectories. These effects produce observable modifications in the relativistic images, including systematic variations in the effective geometry. We also analyze the black hole shadow in relation to current horizon-scale constraints on Sgr~A*. Our results demonstrate that nonlinear electrodynamics can substantially modify photon propagation and relativistic image formation even when the underlying spacetime gometry remains close to the Maxwell electrodynamics case.

We consider off-diagonal asymptotic series for integral kernels of functions of Laplace-type operators on curved backgrounds. These expansions are obtained by applying integral transforms to the DeWitt series for the heat kernel of the corresponding operator and thus represent a DeWitt-type series in the heat kernel coefficients with the coefficients of this expansion (which we call basis kernels) being some hypergeometric-type functions of the Synge world function. Basis kernels of a certain class of operator functions were found previously in terms of $N$-fold Mellin-Barnes integrals. In this paper we study series representations of the corresponding Mellin-Barnes integrals in both non-resonant and resonant cases and suggest a physical interpretation for the emerging series, which is related to the UV and IR properties of operator functions.