Abstract
We compute \( \mathcal{O}(1) \) corrections to the holographic Weyl anomaly for sixdimensional \( \mathcal{N}=\left(1,\ 0\right) \) and (2, 0) theories using the functional Schrödinger method that is conjectured to work for supersymmetric theories on Ricci-flat backgrounds. We show that these corrections vanish for long representations of the \( \mathcal{N}=\left(1,\ 0\right) \) theory, and we obtain an expression for δ(c − a) for short representations with maximum spin two. We also confirm that the one-loop corrections to the \( \mathcal{N}=\left(2,\ 0\right) \) M5-brane theory are equal and opposite to the anomaly for the free tensor multiplet. Finally, we discuss the possibility of extending the results to encompass multiplets with spins greater than two.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz. 43 (1986) 565] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [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].
P. Mansfield and D. Nolland, One loop conformal anomalies from AdS/CFT in the Schrödinger representation, JHEP 07 (1999) 028 [hep-th/9906054] [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 N = 4 SYM/type IIB supergravity correspondence, JHEP 01 (2004) 013 [hep-th/0311021] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, The spectrum of IIB supergravity on AdS 5 × S 5/Z 3 and a 1/N 2 test of AdS/CFT, JHEP 06 (2013) 024 [arXiv:1304.1540] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, 1/N 2 corrections to the holographic Weyl anomaly, JHEP 01 (2014) 002 [arXiv:1310.2611] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, The shortened KK spectrum of IIB supergravity on Y p,q , JHEP 02 (2014) 064 [arXiv:1311.4550] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Higher spins in AdS 5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT, JHEP 11 (2014) 114 [arXiv:1410.3273] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, c − a from the N = 1 superconformal index, JHEP 12 (2014) 145 [arXiv:1407.6024] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, Central charges from the N = 1 superconformal index, Phys. Rev. Lett. 114 (2015) 091603 [arXiv:1411.5028] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP 12 (2014) 031 [arXiv:1407.6061] [INSPIRE].
F. Bastianelli, S. Frolov and A.A. Tseytlin, Conformal anomaly of (2,0) tensor multiplet in six-dimensions and AdS/CFT correspondence, JHEP 02 (2000) 013 [hep-th/0001041] [INSPIRE].
A.A. Tseytlin, R 4 terms in 11 dimensions and conformal anomaly of (2, 0) theory, Nucl. Phys. B 584 (2000) 233 [hep-th/0005072] [INSPIRE].
P. Mansfield, D. Nolland and T. Ueno, Order 1/N 3 corrections to the conformal anomaly of the (2, 0) theory in six-dimensions, Phys. Lett. B 566 (2003) 157 [hep-th/0305015] [INSPIRE].
M. Beccaria, G. Macorini and A.A. Tseytlin, Supergravity one-loop corrections on AdS 7 and AdS 3 , higher spins and AdS/CFT, Nucl. Phys. B 892 (2015) 211 [arXiv:1412.0489] [INSPIRE].
M. Beccaria and A.A. Tseytlin, C T for higher derivative conformal fields and anomalies of (1, 0) superconformal 6d theories, JHEP 06 (2017) 002 [arXiv:1705.00305] [INSPIRE].
M. Beccaria and A.A. Tseytlin, C T for conformal higher spin fields from partition function on conically deformed sphere, JHEP 09 (2017) 123 [arXiv:1707.02456] [INSPIRE].
S.M. Christensen and M.J. Duff, Axial and conformal anomalies for arbitrary spin in gravity and supergravity, Phys. Lett. B 76 (1978) 571 [INSPIRE].
S.M. Christensen and M.J. Duff, New gravitational index theorems and supertheorems, Nucl. Phys. B 154 (1979) 301 [INSPIRE].
P.B. Gilkey, The spectral geometry of a Riemannian manifold, J. Diff. Geom. 10 (1975) 601 [INSPIRE].
T. Parker and S. Rosenberg, Invariants of conformal laplacians, J. Diff. Geom. 25 (1987) 199.
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [hep-th/9712074] [INSPIRE].
V.K. Dobrev, Positive energy unitary irreducible representations of D = 6 conformal supersymmetry, J. Phys. A 35 (2002) 7079 [hep-th/0201076] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for superconformal field theories in 3, 5 and 6 dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
M. Buican, J. Hayling and C. Papageorgakis, Aspects of superconformal multiplets in D > 4, JHEP 11 (2016) 091 [arXiv:1606.00810] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of superconformal symmetry in diverse dimensions, arXiv:1612.00809 [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Anomalies, renormalization group flows and the a-theorem in six-dimensional (1, 0) theories, JHEP 10 (2016) 080 [arXiv:1506.03807] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Conformal anomaly c-coefficients of superconformal 6d theories, JHEP 01 (2016) 001 [arXiv:1510.02685] [INSPIRE].
S. Yankielowicz and Y. Zhou, Supersymmetric Rényi entropy and anomalies in 6d (1, 0) SCFTs, JHEP 04 (2017) 128 [arXiv:1702.03518] [INSPIRE].
A. Lichnerowicz and C. Møller, Propagators and commutators in general relativity, Proc. Roy. Soc. Lond. A 270 (1962) 342.
T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys. A 14 (1999) 41 [hep-ph/9802376] [INSPIRE].
S. Okubo, Modified fourth order Casimir invariants and indices for simple Lie algebras, J. Math. Phys. 23 (1982) 8 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1709.02819
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Liu, J.T., McPeak, B. One-loop holographic Weyl anomaly in six dimensions. J. High Energ. Phys. 2018, 149 (2018). https://doi.org/10.1007/JHEP01(2018)149
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2018)149