Abstract
We compute the \( \mathcal{O} \)(1) contribution to holographic c − a for IIB supergravity on AdS5 × S 5 / \( {{\mathbb{Z}}_n} \) and on AdS5 × T 1,1 / \( {{\mathbb{Z}}_n} \). In both cases, we find agreement with the dual field theory results, thus providing 1/N 2 checks of AdS/CFT with reduced supersymmetry. Since the holographic computation involves a sum over shortened multiplets in the KK tower, we provide some details on the S 5 and T 1,1 spectra in a form that is convenient when considering their \( {{\mathbb{Z}}_n} \) orbifolds. The computation for the even \( {{\mathbb{Z}}_n} \) orbifolds of S 5 includes a sum over the multiplets in the twisted sector that is essential for obtaining agreement with the dual field theory.
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References
D. Anselmi, D. Freedman, M.T. Grisaru and A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
J.T. Liu and R. Minasian, Computing 1/N 2 corrections in AdS/CFT, arXiv:1010.6074 [INSPIRE].
A. Bilal and C.-S. Chu, A note on the chiral anomaly in the AdS/CFT correspondence and 1/N 2 correction, Nucl. Phys. B 562 (1999) 181 [hep-th/9907106] [INSPIRE].
A. Bilal and C.-S. Chu, Testing the AdS/CFT correspondence beyond large-N, hep-th/0003129 [INSPIRE].
P. Mansfield and D. Nolland, Order 1/N 2 test of the Maldacena conjecture: cancellation of the one loop Weyl anomaly, Phys. Lett. B 495 (2000) 435 [hep-th/0005224] [INSPIRE].
P. Mansfield, D. Nolland and T. Ueno, Order 1/N 2 test of the Maldacena conjecture. 2. The full bulk one loop contribution to the boundary Weyl anomaly, Phys. Lett. B 565 (2003) 207 [hep-th/0208135] [INSPIRE].
P. Mansfield, D. Nolland and T. Ueno, The boundary Weyl anomaly in the \( \mathcal{N} \) = 4 SYM/type IIB supergravity correspondence, JHEP 01 (2004) 013 [hep-th/0311021] [INSPIRE].
M. Günaydin and N. Marcus, The spectrum of the S 5 compactification of the chiral N = 2, D = 10 supergravity and the unitary supermultiplets of U(2,2/4), Class. Quant. Grav. 2 (1985) L11 [INSPIRE].
H. Kim, L. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D = 10 supergravity on S 5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Sasaki-Einstein metrics on S 2 × S 3, Adv. Theor. Math. Phys. 8 (2004) 711 [hep-th/0403002] [INSPIRE].
M. Cvetič, H. Lü, D.N. Page and C. Pope, New Einstein-Sasaki spaces in five and higher dimensions, Phys. Rev. Lett. 95 (2005) 071101 [hep-th/0504225] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, The spectrum of IIB supergravity on AdS5 × S 5 / \( {{\mathbb{Z}}_3} \) and a 1/N 2 test of AdS/CFT, JHEP 06 (2013) 024 [arXiv:1304.1540] [INSPIRE].
D. Anselmi and A. Kehagias, Subleading corrections and central charges in the AdS/CFT correspondence, Phys. Lett. B 455 (1999) 155 [hep-th/9812092] [INSPIRE].
S. Christensen and M. Duff, Axial and conformal anomalies for arbitrary spin in gravity and supergravity, Phys. Lett. B 76 (1978) 571 [INSPIRE].
D. Freedman, S. Gubser, K. Pilch and N. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, On the superconformal index of \( \mathcal{N} \) = 1 IR fixed points: a holographic check, JHEP 03 (2011) 041 [arXiv:1011.5278] [INSPIRE].
S. Gukov, Comments on \( \mathcal{N} \) = 2 AdS orbifolds, Phys. Lett. B 439 (1998) 23 [hep-th/9806180] [INSPIRE].
A. Gadde, E. Pomoni and L. Rastelli, The Veneziano limit of \( \mathcal{N} \) = 2 superconformal QCD: towards the string dual of N = 2 SU(N c ) SYM with N f = 2N c , arXiv:0912.4918 [INSPIRE].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS5 × T 11 : predictions on \( \mathcal{N} \) = 1 SCFT’s, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [INSPIRE].
A. Ceresole, G. Dall’Agata and R. D’Auria, KK spectroscopy of type IIB supergravity on AdS5 × T 11, JHEP 11 (1999) 009 [hep-th/9907216] [INSPIRE].
R. Eager, J. Schmude and Y. Tachikawa, Superconformal indices, Sasaki-Einstein manifolds and cyclic homologies, arXiv:1207.0573 [INSPIRE].
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [INSPIRE].
J.T. Liu, P. Szepietowski and Z. Zhao, Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds, Phys. Rev. D 81 (2010) 124028 [arXiv:1003.5374] [INSPIRE].
J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to \( \mathcal{N} \) = 4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [INSPIRE].
K. Skenderis, M. Taylor and D. Tsimpis, A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, JHEP 06 (2010) 025 [arXiv:1003.5657] [INSPIRE].
D. Nolland, AdS/CFT boundary conditions, multitrace perturbations and the c theorem, Phys. Lett. B 584 (2004) 192 [hep-th/0310169] [INSPIRE].
S.S. Gubser and I. Mitra, Double trace operators and one loop vacuum energy in AdS/CFT, Phys. Rev. D 67 (2003) 064018 [hep-th/0210093] [INSPIRE].
S.S. Gubser and I.R. Klebanov, A universal result on central charges in the presence of double trace deformations, Nucl. Phys. B 656 (2003) 23 [hep-th/0212138] [INSPIRE].
T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [INSPIRE].
S. Franco, A. Hanany and A.M. Uranga, Multi-flux warped throats and cascading gauge theories, JHEP 09 (2005) 028 [hep-th/0502113] [INSPIRE].
M. Günaydin, D. Minic and M. Zagermann, 4D doubleton conformal theories, CPT and IIB string on AdS5 × S 5, Nucl. Phys. B 534 (1998) 96 [Erratum ibid. B 538 (1999) 531] [hep-th/9806042] [INSPIRE].
M. Günaydin and N. Warner, Unitary supermultiplets of Osp(8/4, \( \mathbb{R} \)) and the spectrum of the S 7 compactification of eleven-dimensional supergravity, Nucl. Phys. B 272 (1986) 99 [INSPIRE].
M. Bianchi, J.F. Morales and H. Samtleben, On stringy AdS5 × S 5 and higher spin holography, JHEP 07 (2003) 062 [hep-th/0305052] [INSPIRE].
H. Kihara, M. Sakaguchi and Y. Yasui, Scalar Laplacian on Sasaki-Einstein manifolds Y p,q, Phys. Lett. B 621 (2005) 288 [hep-th/0505259] [INSPIRE].
M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons, hep-th/9603167 [INSPIRE].
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Ardehali, A.A., Liu, J.T. & Szepietowski, P. 1/N 2 corrections to the holographic Weyl anomaly. J. High Energ. Phys. 2014, 2 (2014). https://doi.org/10.1007/JHEP01(2014)002
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DOI: https://doi.org/10.1007/JHEP01(2014)002