Recently a remarkable agreement was found between lattice simulations of long Wilson lines and behavior of the Nambu Goto string in flat space-time. However, the latter fails to fit the short distance behavior since it admits a tachyonic mode for a string shorter than a critical length. In this paper we examine the question of whether a classical holographic Wilson line can reproduce the lattice results for Wilson lines of any length. We determine the condition on the the gravitational background to admit a Coulombic potential at short distances. We analyze the system using three different renormalization schemes. We perform an explicit best fit comparison of the lattice results with the holographic models based on near extremal D3 and D4 branes, non-critical near extremal AdS6 model and the Klebanov Strassler model. We find that all the holographic models examined admit after renormalization a constant term in the potential. We argue that the curves of the lattice simulation also have such a constant term and we discuss its physical interpretation.
We study the correlators of two circular Wilson loops of different radii at strong coupling. In our setup one Wilson loop is located inside the other. We use holography to calculate the connected two-point function. Both an AdS background and a confining background are considered. As the computation for the confining case cannot be carried out analytically we solve the problem numerically. In the AdS case our results agree with similar holographic calculations. In the case of a confining background we find an asymptotic area law, in agreement with the result of the lattice strong coupling expa…
N=2* gauge theory in four space-time dimensions arises as a deformation of the parent N=4 supersymmetric Yang-Mill theory under which its hypermultiplet acquires a mass. This theory, on the one hand, has a known supergravity dual and on the other hand is amenable to localization. We explain, using localization, a dynamical selection of the supergravity Coulomb branch vacuum at large N. We also demonstrate that large Wilson loops obey perimeter law, again finding exact match between direct field-theory calculations and string theory. Additionally, we compute free energy at large 't Hooft coupli…
The string theory calculation of the 1/2-BPS circular Wilson loop of N=4 SYM in the planar limit at next to leading order at strong coupling is revisited in the ratio of its semiclassical string partition function and the one dual to a latitude Wilson loop with trivial expectation value. After applying a conformal transformation from the disk to the cylinder, this problem can be approached by means of the Gel'fand-Yaglom formalism. Using results from the literature and the exclusion of zero modes from a modified Gel'fand-Yaglom formula, we obtain matching with the known field theory result. As…
A half-BPS circular Wilson loop in $\mathcal{N}=4$ $SU(N)$ supersymmetric Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this note we utilize the supergravity solutions that are dual to such Wilson loops in a representation with order $N^2$ boxes to calculate this entropy holographically. Employing the matrix model results of Gomis, Matsuura, Okuda and…
We study the expectation values of Wilson-loop operators with the insertionsof local operators Z^J and Zbar^J with large R-charge J from the bulk viewpoint of AdS/CFT correspondence. Classical solutions of strings attached to such deformed Wilson loops at the conformal boundary are constructed and are applied to the computation of Wilson-loop expectation values. We argue that in order to have such solutions for general insertions at finite positions in the base spacetime of the gauge theory, it is crucial to interpret the holographic correspondence in the semi-classical picture as a tunneling …
We study the one-loop effective action of certain classical type IIA string configurations in $AdS_4\times \mathbb{CP}^3$. These configurations are dual to Wilson loops in the $\mathcal{N}= 6\:$ $U(N)_k \times U(N)_{-k}$ Chern-Simons theory coupled to matter whose expectation values are known via supersymmetric localization. We compute the one-loop effective actions using two methods: perturbative heat kernel techniques and full $ζ$-function regularization. We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the $ζ$-…
We study the correlators of the 2d W_N minimal model in the semiclassical regime with large central charge from bulk viewpoint by utilizing open Wilson lines in sl(N) Chern-Simons gauge theory. We extend previous works for the tree level of bulk theory to incorporate loop corrections in this paper. We offer a way to regularize divergences associated with loop diagrams such that three point functions with two scalars and a higher spin current agree with the values fixed by the boundary W_N symmetry. With the prescription, we reproduce the conformal weight of the operator corresponding to a bulk…
We develop a model for hadrons in the framework of the worldline formalism. While being based wholly in four-dimensional quantum field theory, it shares many features with holographic approaches: Already by the use of the worldline formalism the approach appears intrinsically quantum mechanical. As auxiliary fifth dimension Schwinger's proper time is grouped with the physical four spacetime dimensions into an AdS5 geometry, which is warped due to conformal-symmetry breaking effects. Hidden local symmetry is emergent. The four-dimensional sources are extended to five-dimensional fields by a Wil…
We review the study, on the lattice, of the Green-Schwarz gauge-fixed string action describing worldsheet fluctuations about the minimal surface holographically dual to the null cusp Wilson loop, useful to evaluate the cusp anomaly of N = 4 super Yang-Mills (sYM). We comment on discretization, numerical explorations and challenges for the non-perturbative study of this benchmark model of gauge-fixed worldsheet actions.
We use the AdS/SYM correspondence to study the relevant effects of compactified dimensions on the D-brane dynamics. We present a detailed picture of the T-duality transition between branes in type IIA and type IIB supergravity. An analysis of the renormalization scheme coming from the expectation values of background fields and the role of Wilson lines in it is given. We finally explore finite size effects and T-duality maps on the description of Wilson loops by supergravity.
We consider certain 1/4 BPS Wilson loop operators in SU(N) ${\cal N}=4$ supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS5 x S5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving t…
We study planar gluon scattering amplitudes and Wilson loops in non-commutative gauge theory. Our main results are: 1. We find the map between observables in non-commutative gauge theory and their holographic dual. In that map, the region near the boundary of the gravitational dual describes the physics in terms of T-dual variables. 2. We show that in the presence of a large magnetic background and a UV regulator, a planar gluon scattering amplitude reduces to a complex polygon Wilson loop expectation value, dressed by a tractable polarization dependent factor.
Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge theories. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in N=4 super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth -- at most, it can grow a power of `t Hooft coupling. For theory with gauge group SU(N) x SU(N) and bifundamental hypermultiplets, the…
We review certain properties of confinement with added focus on the ones we study with holography. Then we discuss observables whose unique behavior can indicate the presence of confinement. Using mainly the Wilson loop in the gauge/gravity formalism, we study two main features of the QCD string: the string tension dependence on the temperature while in the confining phase, and the logarithmic broadening of the flux tube between the heavy static charges that turns out to be a generic property of all confining theories. Finally, we review the k-string bound state and we show that for a wide cla…
We give a brief expository discussion on the holographic correspondence of correlation functions in the large J limit of AdS/CFT conjecture. We first review our proposals on the interpretation of the so-called GKPW relation in the large J limit or BMN limit, which are based upon a tunneling picture in relating the AdS bulk to its boundary. Some concrete results, explicitly confirming our picture, are summarized. We then proceed to comment on various issues related to this subject, such as extension of the present picture to nonconformal Dp-brane backgrounds, the correlators of deformed Wilson …
Using supersymmetric localization we compute the free energy and BPS Wilson loop vacuum expectation values for planar maximally supersymmetric Yang-Mills theory on $S^d$ in the strong coupling limit for $2\leq d<6$. The same calculation can also be performed in supergravity using the recently found spherical brane solutions. We find excellent agreement between the two sets of results. This constitutes a non-trivial precision test of holography in a non-conformal setting. The free energy of maximal SYM on $S^6$ diverges in the strong coupling limit which might signify the onset of little string…
We provide a brief summary of a method to calculate improvements to the Veneziano Amplitude, creating sub-leading non-linearities in the Regge trajectory of states. We formulate it as an extension of a computation by Makeenko and Olesen. We begin in a confining gauge theory coupled to matter, rewriting the meson scattering amplitude as a specific path integral over shapes and sizes of closed Wilson loops using the worldline formalism. We then prescribe how to further the computation at strong coupling by employing holography, which provides a prescription for the expectation value of these Wil…
It is known that the naive Abelian Wilson loop defined by the Abelian projection cannot reproduce the correct behavior of the double-winding Wilson loop. It is also known that the naive Abelian Wilson loop cannot reproduce the correct behavior of the Wilson loops in higher representations, but this problem was recently solved by using the redefined "Abelian" Wilson loop. In this talk, we will give another reason why this redefined "Abelian" Wilson loop behaves correctly, and by following the same line of the argument, we will propose redefined "Abelian" double-winding Wilson loop which is cons…
We discuss a holographic dual of a non-relativistic (NR) string on AdS5xS5. The NR string can be regarded as a semiclassical string around an AdS2 classical solution corresponding to a straight Wilson line in the gauge-theory side. The quadratic action with respect to the fluctuations is composed of free massive and massless scalars, and free massive fermions on the AdS2 world-sheet. We show that the complete agreement of the spectra between the NR string and a conformal quantum mechanics (CQM). Then we show a holographic relation between normalizable modes of the NR string and wave functions …
It was recently pointed out that the physics of a single discrete gravitational extra dimension exhibits a peculiar UV/IR connection relating the UV scale to the radius of the effective extra dimension. Here we note that this non-locality is a manifestation of holography, encoding the correct scaling of the number of fundamental degrees of freedom of the UV theory. This in turn relates the Wilsonian RG flow in the UV theory to the effective gravitational dynamics in the extra dimension. The relevant holographic c-function is determined by the expression for the holographic bound. Holography in…
We study a novel non-Abelian matrix configuration of probe D-branes in AdS5. This configuration gives rise to a new D-brane phenomenon related to the known "Myers effect" in the context of holography. It is dual to a deformation of the field theory by a Wilson line threaded fermion bilinear. We study the two point function of these short Wilson lines from both the non-Abelian DBI action and a classical string world sheet calculation and identify the region where they agree. We also study a related configuration where the non-Abelian nature of the embedding functions is enhanced by a background…
Inspired by holographic Wilsonian renormalization, we propose a novel perspective on the low-energy effective actions of confining gauge theories with gravity duals. By identifying the IR-boundary value of a certain bulk field as overlapping with the lightest mode of the field theory, we derive its on-shell effective action by integrating over the rest of the geometry. We illustrate the details of this formalism by computing chiral Lagrangian coefficients in a simple AdS/QCD toy model, finding agreement with previous results. At higher orders we obtain new results in that model, including a cl…
We precisely reproduce the perimeter law obeyed by Wilson loops on large spatial contours in planar N=2 SYM at strong coupling, as recently deduced using localization, by means of a dual holographic model. The relevant supergravity background is sourced by D5-branes wrapped on a two-sphere in a Calabi-Yau two-manifold. Thus, localization and holography are cross-checked, for the first time, in a non conformal context where the gravity background is not asymptotically Anti de Sitter and the dual gauge theory has a logarithmically running coupling. We also notice that the same cross-check can be…
We consider large Wilson loops with quarks in higher representations in SU(N) Yang-Mills theories. We consider representations with common N-ality and check whether the expectation value of the Wilson loop depends on the specific representation or only on the N-ality. In the framework of AdS/CFT we show that <W_R> = dim R exp -sigma_k A, namely that the string tension depends only on the N-ality k but the pre-exponent factor is representation dependent. The lattice strong coupling expansion yields an identical result at infinite N, but shows a representation dependence of the string tension at…
We compute the one-loop effective action of string configurations embedded in $AdS_4\times\mathbb{CP}^3$ which are dual to $\frac{1}{6}$-BPS latitude Wilson Loops in the ABJM theory. To avoid ambiguities in the string path integral we subtract the $\frac{1}{2}$-BPS case. The one-loop determinants are computed by Fourier-decomposing the two dimensional operators and then using the Gel'fand-Yaglom method. We comment on various aspects related to the regularization procedure, showing the cancellation of a hierarchy of divergences. After taking into account an IR anomaly from a change in topology,…
Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly.
We compute the non-zero temperature conductivity of conserved flavor currents in conformal field theories (CFTs) in 2+1 spacetime dimensions. At frequencies much greater than the temperature, $\hbarω>> k_B T$, the $ω$ dependence can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these…
The Vafa-Witten arguments on the realization of parity and flavour symmetries in the QCD vacuum do not apply to two lattice regularizations of QCD which are able to reproduce the chiral anomaly: Wilson fermions and Ginsparg-Wilson fermions. We show here how using the last regularization one can get, from first principles, that the more standard order parameters for these symmetries take a vanishing vacuum expectation value for any number of flavours, if quarks have a non-vanishing mass.
A five-dimensional Chern-Simons gravity theory based on the anti-de Sitter group SO(4,2) is argued to be a useful model in which to understand the details of holography and the relationship between generally covariant and dual local quantum field theories. Defined on a manifold with boundary, conformal geometry arises naturally as a gauge invariance preserving boundary condition. By matching thermodynamic quantities for a particular background geometry, the dimensionless coupling constant of the Chern-Simons theory is directly related to the number of fields in a putative dual theory at high t…
We show that the canonical ensemble in any of the six supersymmetric string theories, type IIA and IIB, type IB and type I', or heterotic E_8 x E_8 and Spin(32)/Z_2, exhibits a strong version of holography: the growth of the number of degrees of freedom in the free energy at high temperatures is identical to that in a two-dimensional quantum field theory. We clarify the precise nature of the thermal duality phase transition in each case, confirming that it lies within the Kosterlitz-Thouless universality class. We show that, in the presence of Dbranes, and a consequent Yang-Mills gauge sector,…
We analyze cubic spin 3 interaction in AdS space using the higher spin extension of string-theoretic sigma-model constructed in our previous work, which low energy limit is described by AdS vacuum. We find that, in the leading order of the cosmological constant, the spin 3 correlator on the AdS4 string theory side reproduces the structure of 3 point function of composite operators, quadratic in free fields, in the dual vector model. The cancellation of terms violating higher spin holography is related to the value of the Liouville background charge in four dimensions.
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons and glueballs as strings in four dimensional space time. The models are based on a "map" from stringy hadrons of holographic confining backgrounds. In this note we review the "derivation" of the models. We start with a brief reminder of the passage from the AdS5xS5 string theory to certain flavored confining holographic models. We then describe the string configurations in holographic backgrounds that correspond to a Wilson line,a meson,a baryon and a glueball. The key ingredients of the four d…
We discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding on-shell bulk action reproduces the Wess-Zumino term for the dilaton of broken conformal symmetry, with the expected coefficient aUV-aIR. Then we consider a specific 3D example of RG flow whose UV asymptotics is normalizable and admits a 6D lifting. We promote a modulus ρappearing in the geometry to a function of boundary coordinates. In a 6D description ρ is …
Starting from the non-linear sigma model of the IIB string in the light-cone gauge, we analyze the role of RR fluxes in Holography. We find that the worldsheet theory of states with only left or right moving modes does not see the presence of RR fields threading a geometry. We use this significant simplification to compute part of the strong coupling spectrum of the two dimensional NCOS theory. We also reproduce the action of a closed string in a PP-wave background using this general formalism; and we argue for various strategies to find new systems where the closed string theory may be exactl…
Bilocal holography is a constructive approach to the higher spin theory holographically dual to $O(N)$ vector models. In contrast to other approaches to bulk reconstruction, bilocal holography does not take input from the dual gravitational theory. The resulting map is a complete bulk/boundary mapping in that it maps the complete set of $O(N)$ invariant degrees of freedom in the CFT, to the complete set of higher spin degrees of freedom. After restricting to a suitable code subspace we demonstrate that bilocal holography naturally reproduces the quantum error correcting properties of holograph…
We study four-dimensional Chern-Simons theory on $D \times \mathbb{C}$ (where $D$ is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an "analytically-continued" toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary corre…
We propose a class of ${\rm AdS}_3/{\rm CFT}_2$ dualities with $\mathcal{N}=(2,2)$ supersymmetry. These dualities relate string theory on ${\rm AdS}_3 \times ({\rm S}^3\times \mathbb{T}^4)/{\rm G}$ to marginal deformations of the symmetric product orbifold of $\mathbb{T}^4/{\rm G}$, where ${\rm G}$ is a dihedral group. We demonstrate that the BPS spectrum calculated from supergravity and string theory agrees with that of the dual CFT. Moreover, the supergravity elliptic genus is shown to reproduce the CFT answer, thus providing further non-trivial evidence in favour of the proposal.
We consider Type IIB Neveu-Schwarz five-branes transverse to C^2/Z_n orbifolds and conjecture that string theory on the near horizon geometry is dual to the decoupled theory on the branes. We analyze the conformal field theory describing the near horizon region and the world volume non-critical string theory. The modular invariance consistency condition of string theory is exactly reproduced as the gauge anomaly cancellation condition in the little string theories. We comment on aspects of the holographic nature of this duality.
In this thesis I explore the generality of the holographic principle in 2+1 (bulk) dimensions by looking at the possibility of having holographic correspondences for non-AdS (higher-spin) spacetimes. The first part focuses on Lobachevsky spacetimes with $\mathfrak{sl}(4,\mathbb{R})$ as well as $\mathcal{W}^{(2)}_N$ symmetries, the asymptotic symmetry algebras and their unitary representations. This results in a family of unitary $\mathcal{W}^{(2)}_N$ models that can have both small and large central charge. The focus of the second part is a possible holographic correspondence in asymptotically…
We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for a…
We propose a codimension two holography between a gravitational theory on a $d+1$ dimensional wedge spacetime and a $d-1$ dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain how to compute the free energy, entanglement entropy and correlation functions of the dual CFTs from gravity. In this wedge holography, the holographic entanglement entropy is computed by a double minimization procedure. Especially, for a four dimensional gravity ($d=3$), we obtain a two dimensional CFT and the holographic entanglement entropy perfectly reprod…
We investigate the application of our recent holographic entanglement negativity conjecture for higher dimensional conformal field theories to specific examples which serve as crucial consistency checks. In this context we compute the holographic entanglement negativity for bipartite pure and finite temperature mixed state configurations in $d$-dimensional conformal field theories dual to bulk pure $AdS_{d+1}$ geometry and $AdS_{d+1}$-Schwarzschild black holes respectively. It is observed that the holographic entanglement negativity characterizes the distillable entanglement for the finite tem…
Massive QCD at $θ=π$ breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are su…
In Landau Fermi liquids, screened impurities support quasi-bound states, representing electrons bound to the impurity but making virtual excursions away. Signals of these quasi-bound states are electron-impurity scattering phase shifts and the corresponding resonances in cross sections. We consider large-$N$, strongly-coupled $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory on the Coulomb branch, where an adjoint scalar has a non-zero expectation value that breaks $SU(N) \to SU(N-1) \times U(1)$. In the holographic dual we re-visit well-known solutions for a probe D…
Extremal black branes upon compactification in the near horizon throat region are known to give rise to $AdS_2$ dilaton-gravity-matter theories. Away from the throat region, the background has nontrivial profile. We interpret this as holographic renormalization group flow in the 2-dim dilaton-gravity-matter theories arising from dimensional reduction of the higher dimensional theories here. The null energy conditions allow us to formulate a holographic c-function in terms of the 2-dim dilaton for which we argue a c-theorem subject to appropriate boundary conditions which amount to restrictions…
We show how the BV-BFV formalism provides natural solutions to descent equations, and discuss how it relates to the emergence of holographic counterparts of given gauge theories. Furthermore, by means of an AKSZ-type construction we reproduce the Chern-Simons to Wess-Zumino-Witten correspondence from infinitesimal local data, and show an analogous correspondence for BF theory. We discuss how holographic correspondences relate to choices of polarisation relevant for quantisation, proposing a semi-classical interpretation of the quantum holographic principle.
First we review the derivation of the relativistic flux tube model for a quark-antiquark system from Wilson area law as we have given in a preceding paper. Then we extend the method to the three-quark case and obtain a Lagrangian corresponding to a star flux tube configuration. A Hamiltonian can be explicitly constructed as an expansion in $1 / m^2$ or in the string tension $σ$. In the first case it reproduces the Wilson loop three-quark semirelativistic potential; in the second one, very complicated in general, but it reproduces known string models for slowly rotating quarks.
In this paper we propose a holographic duality for classical gravity on a three-dimensional de Sitter space. We first show that a pair of SU$(2)$ Chern-Simons gauge theories reproduces the classical partition function of Einstein gravity on a Euclidean de Sitter space, namely $\mathbb{S}^3$, when we take the limit where the level $k$ approaches $-2$. This implies that the CFT dual of gravity on a de Sitter space at the leading semi-classical order is given by an SU$(2)$ Wess-Zumino-Witten (WZW) model in the large central charge limit $k\to -2$. We give another evidence for this in the light of…
We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate value of the dynamical critical exponent $z$. In the particular case of 3+1 bulk dimensions and $z=2$ asymptotic scaling near infinity, we find a logarithmic counterterm, related to anisotropic Weyl anomaly of the dual CFT, and show that this counterterm reproduces precisely the …
Holography in flipped AdS/$\mathbb{Z}$: Another approach to dS holography
Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究院、物理科学与技术学院）；School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.
