The Boundary Weyl Anomaly in the   = 4 SYM/Type IIB Supergravity Correspondence

Mansfield, Paul; Nolland, David; Ueno, Takayoshi

doi:10.1088/1126-6708/2004/01/013

Cited by 20 publications

(51 citation statements)

References 16 publications

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“…(2) to a holographic SCFT can also be viewed as a one-loop test of AdS/CFT. In this sense, the result of [15] can be interpreted as a test for the N = 4 theory, confirming and refining the earlier results of [16,17]. This can be easily generalized to the case of arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds.…”

Section: Large-n Theories With Holographic Dualsupporting

confidence: 82%

Central Charges from theN=1Superconformal Index

2015

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We present prescriptions for obtaining the central charges, a and c, of a four dimensional superconformal quantum field theory from the superconformal index. At infinite N , for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the O(1) parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of a and c for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from non-holographic theories for the applicability of these results outside of a holographic setting and away from the large-N limit.

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Section: Large-n Theories With Holographic Dualsupporting

confidence: 82%

Central Charges from theN=1Superconformal Index

2015

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“…First, the quintic polynomial a k follows as well from the generic expression found in [43] and corroborated by explicit zeta regularization in [44]. Second, only the shifted type-B anomaly coefficient turns out to be linear in k and, in consequence, meets the holographic expectation of [56,57] on Ricci-flat backgrounds.…”

Section: Weyl Anomaly For Gjms: Take Isupporting

confidence: 59%

Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

Bugini

Díaz

2019

J. High Energ. Phys.

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The holographic Weyl anomaly for GJMS operators (or conformal powers of the Laplacian) are obtained in four and six dimensions. In the context of AdS/CFT correspondence, free conformal scalars with higher-derivative kinetic operators are induced by an ordinary second-derivative massive bulk scalar. At one-loop quantum level, the duality dictionary for partition functions entails an equality between the functional determinants of the corresponding kinetic operators and, in particular, it provides a holographic route to their Weyl anomalies. The heat kernel of a single bulk massive scalar field encodes the Weyl anomaly (type-A and type-B) coefficients for the whole tower of GJMS operators whenever they exist, as in the case of Einstein manifolds where they factorize into product of Laplacians. While a holographic derivation of the type-A Weyl anomaly was already worked out some years back, in this note we compute holographically (for the first time to the best of our knowledge) the type-B Weyl anomaly for the whole family of GJMS operators in four and six dimensions. There are two key ingredients that enable this novel holographic derivation that would be quite a daunting task otherwise: (i) a simple prescription for obtaining the holographic Weyl anomaly for higher-curvature gravities, previously found by the authors, that allows to read off directly the anomaly coefficients from the bulk action; and (ii) an implied WKB-exactness, after resummation, of the heat kernel for the massive scalar on a Poincaré-Einstein bulk metric with an Einstein metric on its conformal infinity. The holographically computed Weyl anomaly coefficients are explicitly verified on the boundary by exploiting the factorization of GJMS operators on Einstein manifolds and working out the relevant heat kernel coefficient. §

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“…The reason for this −1 contribution can be understood also by giving vector a mass by coupling it to a complex scalar so that it will not contribute to c; then the central charge of the scalar part is reduced by 1 as one scalar component is absorbed by the vector. 8 The same result is found by counting the SU(2) chiral anomaly of the (4, 4) superconformal algebra [13,12]. 9 The (4, 4) vector multiplet contains one 2d vector A m , 4 scalars φ i , 4 real spinors ψ k and 3 auxiliary fields D r , all having canonical dimensions (i.e.…”

Section: Ads 3 /Cftsupporting

confidence: 58%

Supergravity one-loop corrections on AdS 7 and AdS 3 , higher spins and AdS/CFT

2015

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As was shown earlier, the one-loop correction in 10d supergravity on AdS 5 × S 5 corresponds to the contributions to the vacuum energy and 4d boundary conformal anomaly which are minus the values for one N = 4 Maxwell supermultiplet, thus reproducing the subleading term in the N 2 − 1 coefficient in the dual SU(N ) SYM theory. We perform similar one-loop computations in 11d supergravity on AdS 7 × S 4 and 10d supergravity on AdS 3 × S 3 × T 4 . In the AdS 7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2, 0) tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2, 0) theory is 4N 3 − 9/4N − 7/4 and thus vanishes for N = 1. In the AdS 3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4, 4) scalar multiplet, i.e. is c = +6. This reproduces the subleading term in the central charge c = 6(Q 1 Q 5 + 1) of the dual 2d CFT describing decoupling limit of D5-D1 system. We also present the expressions for the 6d a-anomaly coefficient and vacuum energy contributions of general-symmetry higher spin field in AdS 7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank-2 antisymmetric tensors.

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The Boundary Weyl Anomaly in the = 4 SYM/Type IIB Supergravity Correspondence

Cited by 20 publications

References 16 publications

Central Charges from theN=1Superconformal Index

Central Charges from theN=1Superconformal Index

Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

Supergravity one-loop corrections on AdS 7 and AdS 3 , higher spins and AdS/CFT

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