Partition functions for higher-spin theories in AdS

Gupta, Rajesh Kumar; Lal, Shailesh

doi:10.1007/jhep07(2012)071

Cited by 42 publications

(65 citation statements)

References 41 publications

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“…One expands the metric g around the AdS background which is taken the same (static) solution as the AdS vacuum g = g AdS + η. In [30,31], the partition functions of higher spin theories in odd dimensional AdS spaces are explicitly calculated using the heat kernel method. One can follow exactly the same method in performing the calculations in AdS 4 .…”

Section: The Heat Kernel Methodsmentioning

confidence: 99%

1/Nand loop corrections in higher spinAdS4/CFT3
Jevicki
¹
,
Jin
²
,
Yoon
³

2014
Phys. Rev. D
29
3
39
0
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Abstract:We consider the question of loop corrections (i.e. 1/N ) in the vector model/higher spin duality following the recent work of Giombi and Klebanov [1]. The purpose of this paper is to gain further more precise comparison between the two sides of the duality. For CFTs given by 3d O(N ) or U (N ) vector models we evaluate the leading and one loop partition functions in a variety of geometries. Our calculations are performed in the scheme of collective field theory which was seen in earlier studies to represent a bulk description of Vasiliev higher spin theory. The calculations presented provide data for comparison of small fluctuation determinants giving further evidence for the one-to-one bulk identification between the bilocal and the AdS picture. They also offer insight into the identification of coupling constants G and 1/N of the two descriptions for models based on O(N ) symmetry.

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Section: The Heat Kernel Methodsmentioning

confidence: 99%

1/Nand loop corrections in higher spinAdS4/CFT3
Jevicki
¹
,
Jin
²
,
Yoon
³

2014
Phys. Rev. D
29
3
39
0
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“…Upon gauge fixing the linearized gauge invariance of the quadratic action, the contribution to the one-loop partition function of each massless field of spin s is given by the ratio of determinants [52][53][54] Z s = det…”

Section: The Higher-spin Spectral Zeta Functionmentioning

confidence: 99%

Higher spinAdSd+1/CFTdat one loop

2014

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Following [1], we carry out one loop tests of higher spin AdS d+1 /CFT d correspondences for d ≥ 2. The Vasiliev theories in AdS d+1 , which contain each integer spin once, are related to the U (N ) singlet sector of the d-dimensional CFT of N free complex scalar fields; the minimal theories containing each even spin once -to the O(N ) singlet sector of the CFT of N free real scalar fields. Using analytic continuation of higher spin zeta functions, which naturally regulate the spin sums, we calculate one loop vacuum energies in Euclidean AdS d+1 . In even d we compare the result with the O(N 0 ) correction to the a-coefficient of the Weyl anomaly; in odd d -with the O(N 0 ) correction to the free energy F on the d-dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of N free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in d dimensions. As explained in [1], this result may agree with the O(N ) singlet sector of the theory of N real scalar fields, provided the coupling constant in the higher spin theory is identified as G N ∼ 1/(N −1). Our calculations in even d are closely related to finding the regularized a-anomalies of conformal higher spin theories. In each even d we identify two such theories with vanishing a-anomaly: a theory of all integer spins, and a theory of all even spins coupled to a complex conformal scalar. We also discuss an interacting UV fixed point in d = 5 obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large N theory is dual to the Vasiliev theory in AdS 6 where the bulk scalar is quantized with the alternate boundary condition.

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“…The analytic continuation acress the quotient spaces should account for these differences, but once that is done, completely consistent answers are obtained. See for example [44][45][46].…”

Section: )mentioning

confidence: 99%

“…To evaluate the path integral, we will fix gauge by adding the term 45) so that the total action becomes…”

Section: The Hodge Laplacian For Vector Fieldsmentioning

confidence: 99%

Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy

Gupta

Lal

Thakur

2014

J. High Energ. Phys.

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We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z N orbifold of the nearhorizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z N orbifolds of higher-dimensional spheres and hyperboloids.

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Partition functions for higher-spin theories in AdS

Cited by 42 publications

References 41 publications

1/Nand loop corrections in higher spinAdS4/CFT3
Jevicki
¹
,
Jin
²
,
Yoon
³

2014
Phys. Rev. D
29
3
39
0
View full text Add to dashboard Cite

1/Nand loop corrections in higher spinAdS4/CFT3
Jevicki
¹
,
Jin
²
,
Yoon
³

2014
Phys. Rev. D
29
3
39
0
View full text Add to dashboard Cite

Higher spinAdSd+1/CFTdat one loop

Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy

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Partition functions for higher-spin theories in AdS

Cited by 42 publications

References 41 publications

1/Nand loop corrections in higher spinAdS4/CFT3Jevicki1, Jin2, Yoon3 2014Phys. Rev. D293390View full textAdd to dashboardCite

1/Nand loop corrections in higher spinAdS4/CFT3Jevicki1, Jin2, Yoon3 2014Phys. Rev. D293390View full textAdd to dashboardCite

Higher spinAdSd+1/CFTdat one loop

Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy

Contact Info

Product

Resources

About

1/Nand loop corrections in higher spinAdS4/CFT3
Jevicki
¹
,
Jin
²
,
Yoon
³

2014
Phys. Rev. D
29
3
39
0
View full text Add to dashboard Cite

1/Nand loop corrections in higher spinAdS4/CFT3
Jevicki
¹
,
Jin
²
,
Yoon
³

2014
Phys. Rev. D
29
3
39
0
View full text Add to dashboard Cite