Papers

We derive a concrete closed string dual to any interacting Hermitian one-matrix model, away from the double-scaling limit. Matrix and string correlators manifestly agree, to all orders in the genus expansion and all orders in the 't Hooft coupling(s). The worldsheet theory consists of a supersymmetric B-twisted Landau-Ginzburg model coupled to 2d topological gravity. We provide a precise dictionary between traces of the matrix and vertex operators on the worldsheet. Matrix model correlators are explicitly mapped to computable integrals over the moduli space of Riemann surfaces. We perform several direct cross-checks on both sides of the duality. This work furnishes a detailed instantiation of gauge/string duality, in the standard 't Hooft regime, and hopefully a useful worldsheet toy model for the AdS/CFT correspondence, away from the free field limit.

We derive quantum gravity contributions to the beta functions of the gauge and Yukawa couplings of a matter theory using the Schwinger proper-time flow equation. Working in the Einstein-Hilbert truncation, we investigate the gauge-fixing and regulator dependence of the corresponding renormalization group equations. We quantify the sensitivity of our results on unphysical parameters by evaluating the gravitational correction to the running matter couplings at the interactive fixed point of gravity and we compare our findings with existing determinations in alternative schemes. We finally confront the derived contributions with the typical size they should assume to generate observable low-scale predictions in the Standard Model and in several scenarios of new physics.

An infinite family of integrable vortex equations is studied and related to the Cartan geometry of the underlying Riemann surfaces. This Cartan picture gives an interpretation of the vortex equations as the flatness of a non-Abelian connection. Solutions of the vortex equations also give rise to magnetic zero-modes for a certain Dirac operator on the lifted geometry. The family of integrable vortex equations is parametrised by a positive number $n$, that is equal to unity in the standard case and an integer in the case of polynomial vortex equations; finally, it may be extended to any positive real number.

Planar AdS black branes have a scaling symmetry that maps a brane solution at one temperature to a solution at another. It is natural to expect that boundary representations of bulk field modes should inherit this symmetry i.e. their correlators should transform covariantly under boundary dilatations. We derive a covariance condition that any boundary representation of interior modes in a planar AdS black brane should satisfy. We then show that Papadodimas-Raju mirror operators satisfy this condition. Thus the Papadodimas-Raju reconstruction of the bulk interior, although state-dependent, inherits the scaling symmetry of planar AdS black holes.

Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer exact stationary points of the Euclidean action, in contrast to the symmetric phase. Non-perturbative effects in this setting are therefore typically studied within the constrained instanton framework. However, a previous study pointed out a possible difficulty in constructing consistent constrained instanton solutions based on conventional gauge-invariant constraints. In this work, we revisit the asymptotic structure of constrained instantons and re-examine the claimed difficulty. By carefully tracking the behavior of the solutions near the spatial origin and at infinity, we show that the required boundary conditions can be satisfied without encountering the inconsistency. We explicitly construct consistent constrained instantons in both massive $\phi^4$ theory and Yang–Mills theory with spontaneous symmetry breaking, and we support our analytic matching procedure with numerical solutions. Our results establish that conventional gauge-invariant constraints can be consistently employed in semiclassical computations when asymptotic expansions are treated properly.

We present the first complete calculation of the analytic structure of the zero-spatial-momentum finite-temperature Landau-gauge gluon propagator carried out at one loop by a massive deformation of QCD perturbation theory – the screened massive expansion – at temperatures ranging from $T=0$ to $T\approx 3T_{c}$. We find no signatures of deconfinement in the form of meaningful changes in said structure. We argue that, beyond Euclidean space, massive perturbative methods – including the Curci-Ferrari model – might be missing crucial dynamical information as a consequence of the perturbative violation of QCD's Ward identities.

We classify extended Abelian Chern-Simons theories with gauge group $U(1)^n$ as extended $(2+1)$-dimensional topological quantum field theories. For an even integral nondegenerate lattice $(\Lambda,K)$, let $(G_K,q_K)$ denote its discriminant quadratic module. We prove that the associated theory is determined, up to symmetric monoidal natural isomorphism, by this finite quadratic module, and that every finite quadratic module is realized as the discriminant quadratic module of an even integral nondegenerate lattice. It follows that finite quadratic modules classify extended Abelian Chern-Simons theories, pointed Abelian Reshetikhin-Turaev TQFTs, and pointed modular tensor categories.

Describing the proton structure function $F_2(x,Q^2)$ across the nonperturbative and transition regimes of QCD remains a major theoretical challenge. We construct a physics-guided phenomenological representation combining fermion-resonance and Pomeron-like AdS/QCD basis functions with a neural parametrization. The resonance sector is constrained by the AdS eigenvalue problem and physical proton mass, while the neural component describes effective kinematic mixing, Pomeron normalization, and a regularized log-space correction. For 187 selected SLAC measurements, a fixed 153/34 training–test split gives $\chi^2/N_{\rm train}=0.542$, $\chi^2/N_{\rm test}=1.990$, and $\chi^2/N_{\rm all}=0.805$. Conditional on the chosen holographic basis, the fitted channel fractions evolve continuously from Pomeron-like dominance at lower measured $x$ to fermion-resonance dominance at larger $x$. The mixing midpoint is at $x\simeq0.187$, while equality of the final channel fractions occurs at $x\simeq0.226$, defining a transition region $x\simeq0.19$–$0.23$ rather than a unique boundary. Although $\alpha_0\simeq1.08$ is compatible with the data, fixed-$\alpha_0$ refits show that it is not separately identifiable from the flexible Pomeron normalization. The $x$-dependent holographic coordinates and effective excited scales should therefore be regarded as basis-dependent quantities rather than direct measurements of an $x$-dependent proton spectrum. A data-only neural baseline shows no predictive advantage for the holographic basis on the present dataset. The framework thus provides a basis-conditioned phenomenological decomposition rather than a model-independent extraction of proton dynamics.

We show that the notion of a black hole mass could be superceded by that of a topological charge in a spacetime without matter and curvature singularity. This feature emerges through a set new spacetime solutions of first order gravity in vacuum, named as bubble spacetimes, constructed here by weaving together the degenerate and nondegenerate metric phases. For a static bubble, the boundary surface connecting the two phases is characterized by a universal topological number. Notably, this surface coincides with the photon sphere of the conventional black hole irrespective of the presence of the cosmological constant. In contrast, a phase boundary located at the event horizon is shown to be topologically trivial. Thus, along with the black hole mass, the photon sphere also acquires a topological interpretation.

't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by $\sim a_1\wedge a_2\wedge a_3\wedge a_4$, where the $a_i$ denote background gauge fields for the global symmetries. Through explicit lattice gauging, we demonstrate the emergence of higher symmetry structures, including 2-group, non-invertible, and higher fusion categorical symmetries. We also provide a field-theoretical understanding of these results. Applying this framework to systems with Lieb-Schultz-Mattis anomalies, obtained by promoting part of the internal symmetries to translational symmetries, we demonstrate that modulated (dipole) symmetries arise as direct counterparts of those in systems with purely internal typeIV anomalies. Importantly, we uncover a qualitatively new feature absent in previously studied modulated symmetries: their realization can become intrinsically defect-dependent. In particular, the emergent symmetry structure changes depending on whether symmetry defects are present. This work establishes a concrete lattice realization of mixed anomalies and reveals a rich structure of emergent symmetries, thereby clarifying their role in constraining quantum phases of matter.

We argue that the topological structure of Abelian gauge theories, such as Maxwell electrodynamics, in the background of a Euclidean Schwarzschild black hole manifests itself through an asymmetry in Hawking radiation. In particular, the topology of the black hole manifold, characterised by a non-contractible 2-sphere and Euler characteristic $\chi = 2$, admits non-trivial gauge-field configurations. These take the form of 2-form field strengths that are closed but not exact. From a topological perspective, such configurations are classified by the second cohomology group, which is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$, and are labelled by integer electric ($n$) and magnetic ($m$) charges, $(n,m)$. Self-dual ($n = m$) and anti-self-dual ($n = -m$) dyonic configurations carry vanishing Euclidean energy and are fully compatible with the Euclidean Schwarzschild geometry. More general dyonic configurations, by contrast, are interpreted as off-shell Euclidean field configurations. Nevertheless, both classes contribute to the thermal equilibrium vacuum and to finite-temperature correlation functions in the corresponding Lorentzian framework. Furthermore, because of the non-trivial topology, the electromagnetic $\theta_{\rm EM}$-term contributes to the physical observables. In particular, it sources $CP$-asymmetric Hawking radiation, observable as an imbalance between left- and right-polarised photons in the emission spectrum. We briefly discuss some implications of this phenomenon.

We study QED$_2$ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as $1/a(t)$ while the electric term grows as $g^2 a(t)$, sweeping the spectrum through a moving narrow-gap region in the $(\tau,m)$ plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later $\tau$ as the lattice spacing goes to zero, with current data favoring $\tau_* \approx 3.1$, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED$_2$ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

Recent claims have suggested the absence of CP violation in theories with a $\theta$-vacuum structure, particularly in quantum chromodynamics. We highlight several key points, from a perspective that is not widely discussed in the literature, which clarify why such conclusions are incorrect. In particular, an open boundary in a finite-volume theory must be accompanied by boundary degrees of freedom, the edge modes, in order to preserve large gauge invariance and faithfully capture the topological features of the theory. In the infinite-volume limit, these edge states become non-dynamical, leaving the standard $\uptheta$-vacuum structure intact, irrespective of whether this limit is taken before or after summing over topological sectors. Consequently, the $\uptheta$-vacuum structure does give rise to observable CP violation once the theory is consistently quantised.

This paper is concerned with eternal AdS black holes. The quantum cosmological future and past interior states of the black hole may be placed on an equal footing to the left and right AdS boundary data by considering the on-shell bulk action as a function of the left/right/future/past data: $S[\phi^{(0)L},\phi^{(0)R},\phi^{(0)F},\phi^{(0)P}]$. We call this object a holographic banner, and it obeys the Hamilton-Jacobi equation with respect to all four of its arguments. We compute the holographic banner for a scalar field in an AdS black hole background explicitly and use it to construct the semiclassical state in the future interior obtained from a thermofield double state in the past evolved by arbitrary time- and space-dependent boundary sources. When the spacetime itself is dynamical we explain how the holographic banner gives, in principle, a map from boundary data to near-singularity semiclassical quantum cosmology following chaotic BKL dynamics. We obtain the timescale for the BKL dynamics to ergodically mix the future interior quantum state, given a quantum variance in the past state or a classical ensemble of boundary theories.

In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ ($0\leq \gamma \leq 1$), where $\gamma=1$ represents a stiff or Zeldovich fluid. Using Marder's metric with coefficients depending on $t$ and $r$, we obtain explicit solutions of the gravitational field equations for the three cases $\delta = 1, 0, -1$, corresponding to exponential, power-law, and trigonometric behaviors of the metric functions. The resulting space-times exhibit anisotropic evolution, nontrivial expansion and shear, and curvature singularities, with energy density and pressure profiles determined by the integration constants. These solutions provide a comprehensive framework for modeling cylindrically symmetric cosmologies, offering insights into early-universe dynamics and anisotropic gravitational phenomena. The versatility of the solutions also opens avenues for extensions to higher-dimensional or modified gravity scenarios, making them a valuable tool for both theoretical and phenomenological studies in general relativity.

Symmetric mass generation (SMG) has attracted growing interest in both condensed matter theory and lattice-QCD communities. Here we formulate general criteria for SMG and examine their compatibility with lattice-QCD. We propose possible RG-flow scenarios near the SMG transition, and argue that meson mass ratio can serve as a probe of the SMG transition viewed as a UV fixed point. We further identify Goldstone tetraquark meson states as phenomenological signatures of the "type-II” SMG phase.

Vacuum fluctuations of quantum fields provide an unavoidable environment for any quantum system coupled to it. We study the interplay between boundary conditions and acceleration in determining decoherence of a two-level Unruh-DeWitt detector coupled to a scalar field in a cylindrical cavity. We show that the decoherence rate closely follows the emission profile, and exhibits Purcell-like enhancement for both inertial and uniformly accelerated detectors. The acceleration induces an effective smearing of the resonant density of states, diluting the resonance enhancement for large accelerations while replacing the inertial off-resonant decay with an oscillatory behavior for small accelerations. For moderate accelerations, this interplay between cavity-induced and acceleration-assisted effects results in an extended region of cavity parameters where decoherence is strongly suppressed, particularly in regimes where the inertial detector otherwise experience strong decoherence. Thus, contrary to naive expectations, the Unruh thermality in a suitably engineered cavity can enhance rather than degrade quantum coherence, providing a very uncharacteristic feature of quantum fields in non-inertial frames.

We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body observables. In contrast to previous rigorous results on thermalization with semiclassical counterparts, our method is not limited to statistical averages of observables, such as time averages in ergodicity or state averages in mixing. Moreover, consistent with such approaches, we retain the advantage of not requiring a detailed knowledge of energy eigenstate structure or thermodynamically large times, which can become intractable for systems with more than a handful of particles. Our approach is centered on a geometric result that connects thermalization to the alignment of high dimensional subspaces in a Hilbert space, which is determined by the saturation of "controllably nonlocal" out-of-time-ordered correlators. We discuss the possibility of predicting quantum thermalization in almost all states at almost all times from finite-time observations of a single such correlator per observable. This formalism reduces the problem of establishing pure state quantum thermalization at finite times in almost all complex many-body states to a theoretically or experimentally accessible study of few-body correlators, even in thermodynamically large systems.

Dijkgraaf-Witten theories have a wide range of applications in topological phases of matter and the study of generalized global symmetries. We develop a method to construct BF-type Lagrangians for Dijkgraaf-Witten theories with non-abelian gauge group by gauging $H^{(0)}$ symmetries from a BF-Lagrangian of an abelian Dijkgraaf-Witten theory. When $H$ nontrivially permutes the operators of the original theory, the Lagrangian of the $H$-gauged theory is constructed with cohomologies with local coefficients. We analyze the structure of the Lagrangians and their gauge transformations with homotopy theory. We also construct the operator spectrum and verify the Lagrangians by matching elementary linking invariants.

We present a holographic construction of the QCD axion based on a warped 5D model. A key ingredient of our setup is the introduction of a bulk scalar field $\theta$, which is holographically dual to the topological operator of QCD. This makes the relation among the axion, the $\eta'$, and the anomalies transparent. We identify the bulk modes corresponding to the $\eta'$ and axion states, and show that an adjustment analogous to that of the usual 4D axion takes place. We identify the origin of the axion quality problem in this framework and show that a large degree of axion compositeness is needed to solve it. We also find that, in the limit of a high quality axion, the physical axion state is predominantly contained in the bulk gauge field.

Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii–Kosterlitz–Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on $S^1$, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement of the current algebra at self-dual radius, and non-geometric T-fold transition functions.

Symmetry and entanglement are two fundamental concepts in quantum many-body physics. Their interplay is captured by symmetry-resolved entanglement, which decomposes the total entanglement into contributions from different symmetry sectors. Computing symmetry-resolved entanglement in strongly interacting higher-dimensional quantum systems remains challenging. Here, we formulate and implement an estimator-based quantum Monte Carlo (QMC) framework for computing symmetry-resolved Rényi entropies (SRRE) in sign-problem-free interacting lattice systems by measuring disorder (symmetry-twisted) operators in ordinary and replica ensembles and reconstructing SRRE from the corresponding charged moments. We validate the framework in two controlled one-dimensional settings: the transverse-field Ising model (TFIM), for which exact conformal-field-theory predictions are available, and the interacting Heisenberg chain, which tests the $U(1)$ symmetry-sector reconstruction and its finite-size behavior. We then apply the method to the two-dimensional TFIM. Within the accessible system sizes and a phenomenological finite-size extrapolation, our data provide numerical evidence consistent with entanglement equipartition at the $(2+1)$D Ising critical point. Our work establishes a practical numerical route to symmetry-resolved entanglement in interacting lattice models and provides a framework for future studies beyond one dimension.

Models of gravity in warped extra dimensions enjoy invariance under diffeomorphism. We derive the nonlinear transformation rules for the metric perturbations in the unitary gauge. As an off-shell symmetry, the main consequence of diffeomorphism is a set of recursive relations linking consecutive orders in the field expansion of the effective Lagrangian. The physical consequences are briefly explored for the Randall-Sundrum model with hard branes.

Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by its entanglement spectrum, invariants of multipartite entanglement structures are comparatively difficult to define and work with. The root cause of this difference is that the bipartite problem can be reduced to the analysis of matrix invariants, while its multipartite version is governed by a much richer space of tensor invariants. The present work explores the latter through the lens of so-called trace-invariants, which are in one-to-one correspondence with combinatorial objects known as colored graphs. We first explain why trace-invariant evaluations can serve as labels of LU-orbits of multipartite pure states, how this strategy extends to random states, and how the effect of local operations (LO) can be analyzed through such data. We then focus on entanglement classification within an (infinite-dimensional) subspace of reference states, whose basic building blocks are GHZ states of various dimensions. We show that relatively simple subclasses of trace-invariants are sufficient to separate the LU-orbits of reference states, and enable a complete (resp. an incomplete) characterization of their relations in the LO (resp. LOCC) resource theory of entanglement. Finally, we investigate how a (still infinite) subclass of reference states of local dimension N can be efficiently distinguished at leading and subleading orders in an asymptotic large-N expansion (among themselves, or from Haar-random states). This analysis relies crucially on combinatorial quantities associated to colored graphs, some of which have already played instrumental roles in the recent literature on random tensors. Results of broader relevance are reported along the way.

We quantize the degrees of freedom on a gravitational null ray segment in a fully gauge-invariant manner by using the dressing time as a quantum reference frame (QRF). Our work goes beyond previous models in that the QRF we employ is made out of the gravitational field itself, and accounts for the full group of diffeomorphisms along the ray, not just a locally compact subgroup. The key tool we introduce is covariant normal ordering, a QRF-dependent but background-independent renormalization prescription that restores diffeomorphism covariance at the quantum level. This enables the definition of a quantum dressing map whose image is the algebra of gauge-invariant observables. We find that this algebra carries the structure of a Virasoro crossed product, and that the dressing map induces a deformed product on gauge-fixed operators which can be understood as a quantization of the Dirac bracket, with consequences for the fluctuations of observables. We explain how to cancel anomalies in the physical Hilbert space representation of the gauge-invariant algebra by including a deformation at the classical level, thereby eliminating all spurious degrees of freedom at the quantum level. The physical Hilbert space admits a Page-Wootters reduction map to the perspective of the dressing time, and we show that the dressing time is non-ideal in the sense that its distinct coherent states have non-vanishing overlaps governed by the Teo-Takhtajan energy, i.e. the Kähler potential for Virasoro coadjoint orbits.

Employing the Schwinger-Keldysh formalism, we formulate an effective field theory for s-wave superconducting phase transition, where the dynamical variables consist of electromagnetic gauge field and complex scalar order parameter. Symmetry-constrained effective action allows systematic handling of dissipations and fluctuations. In particular, we explore the physical implications of higher-order terms, including those involving additional dynamical fields as well as higher time derivatives, on the real-time dynamics near the superconducting critical point. When appropriately truncated, the effective field theory reproduces the phenomenological Ginzburg-Landau equations. Upon crossing the critical temperature into the low-temperature phase, the electromagnetic gauge symmetry undergoes spontaneous breaking induced by the condensate of the order parameter. Collective excitation analysis reveals that the Higgs mode behaves as an overdamped diffusive mode near the critical point, while the phase fluctuation is absorbed into the gauge field via the Higgs mechanism. Via the holographic Schwinger-Keldysh technique, rigorous validation in a holographic superconductor confirms the structure of the effective action and quantifies the Wilsonian coefficients. Holographic results revaeal a complex relaxation parameter that indicates oscillatory dynamics characteristic of strongly coupled systems.

We investigate the symmetry structure of the $3+1$ D staggered fermion Hamiltonian and its implications for anomalies. Since the spin and flavor degrees of freedom of Dirac fermions are distributed over the lattice, in addition to the standard on-site mass term, the staggered fermion system also admits one-, two-, and three-link bilinear terms within a unit cube as local, charge conserving mass terms with different spin and flavor dependence. We identify the spin flavor structures of all those bilinear mass terms and determine the symmetries preserved by each of them. Among them, one of the one-link mass terms preserves a larger residual symmetry associated with conserved charges that generate the Onsager algebra. Motivated by this structure, we consider a kink profile of the one-link mass and analyze the resulting domain-wall system. In the low-energy limit, the $3+1$ D bulk becomes gapped, while two-flavor massless Dirac fermions appear as localized modes on the $2+1$ D domain wall. We show that the bulk conserved charges act on the wall as generators of a flavor $\mathrm{SU}(2)$ symmetry, and that no symmetric mass gap is allowed for the boundary theory when this $\mathrm{SU}(2)$ symmetry and space reflection symmetry are both imposed. This realizes the parity anomaly of the boundary theory and shows that the boundary flavor symmetry and anomaly descend from the ultraviolet staggered-fermion Hamiltonian rather than emerging only in the infrared.

In this paper, based on noncommutative-geometry-inspired Schwarzschild black hole, we employ a third-order WKB approximation approach to systematically calculate the quasinormal mode frequencies (QNFs), greybody factors (GFs), and absorption cross section (ACS) under massive scalar field perturbations. The results show that the QNFs satisfy Im($\omega$)<0, confirming the stability of the black hole under perturbations. Furthermore, increasing the noncommutative parameter $\theta$ reduces the absolute values of both the real and imaginary parts of the frequency, while increasing mass $\mu$ increases the real part and reduces the imaginary part. The GFs and ACS increase with increasing $\theta$ and decrease with increasing $\mu$, indicating opposite modulation effects of these two types of parameters. It is worth emphasizing that the QNFs of the extreme black hole approach the corresponding values of the classical Schwarzschild black hole at angular quantum number $\ell=1$ and large $\mu$, suggesting that, the effects of mass and noncommutative geometry quantum corrections cancel each other out to some extent. It is hoped that these results provide a viable theoretical basis for both the theoretical and experimental aspects of the perturbative dynamics of black hole.

We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/\Lambda \cong U(1)^n$ at level $K$, where $K:\Lambda\times\Lambda\to\mathbb Z$ is an even, integral, nondegenerate symmetric bilinear form, by exact zeta-regularized Gaussian evaluation of the formal quotient integral over connections modulo gauge. For closed $3$-manifolds, this yields a topological invariant; for manifolds with boundary, the relative functional integral produces the canonical boundary state. The resulting theory satisfies the required axioms of a $(2+1)$-dimensional TQFT.

In this work, we investigate the worldsheet symmetry of bosonic brane theories and its quantum consistency in the tensionless limit. We find that the residual worldsheet symmetry after specific gauge fixing is generated by a novel algebra, denoted as $g^{(p)}_\lambda$. To achieve full quantization of the tensionless brane, we introduce a $bc$ ghost system and derive the overall BRST charge. Moreover, we calculate the quantum anomaly of the $g^{(p)}_\lambda$ algebra for general parameters $p$ and $\lambda$ in the framework of canonical quantization. After demanding that this quantum anomaly vanishes, we derive the critical dimensions of the bosonic brane theories. Especially, we obtain nontrivial solutions for the tensionless string: $D=14$ spacetime dimensions when $\lambda=-1$ and $D=26$ spacetime dimensions when $\lambda=1$. We also notice that the quantum anomaly automatically vanishes after the Riemann zeta function regularization for $p>1$. This is consistent with the mathematical fact that there is no scalar central extension of the algebra $g^{(p)}_\lambda$ for $p>1$.