We systematically analyze the effective action on the moduli space of (2, 0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four dimensions. We present a streamlined approach to non-renormalization theorems that constrain this effective action. The first several orders in its derivative expansion are determined by a one-loop calculation in five-dimensional Yang-Mills theory. This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2, 0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2, 0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2, 0) supersymmetry, thereby establishing the a-theorem for this class of theories. Along the way, we encounter various field-theoretic arguments for the ADE classification of (2, 0) theories.
Conformal Field Theory Extended Supersymmetry M-Theory Supersym- metric Effective Theories
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
S. Paban, S. Sethi and M. Stern, Constraints from extended supersymmetry in quantum mechanics, Nucl. Phys.B 534 (1998) 137 [hep-th/9805018] [INSPIRE].
M. Dine and N. Seiberg, Comments on higher derivative operators in some SUSY field theories, Phys. Lett.B 409 (1997) 239 [hep-th/9705057] [INSPIRE].
K.A. Intriligator, Anomaly matching and a Hopf-Wess-Zumino term in 6d, N = (2, 0) field theories, Nucl. Phys.B 581 (2000) 257 [hep-th/0001205] [INSPIRE].
J.L. Cardy, Is There a c Theorem in Four-Dimensions?, Phys. Lett.B 215 (1988) 749 [INSPIRE].
E. Witten, Some comments on string dynamics, in Future perspectives in string theory. Proceedings, Conference, Strings’95, Los Angeles, U.S.A., 13–18 March 1995, pp. 501–523 (1995) [hep-th/9507121] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Anomalies, renormalization group flows and the a-theorem in six-dimensional (1, 0) theories, JHEP10 (2016) 080 [arXiv:1506.03807] [INSPIRE].
E. Witten, Conformal Field Theory In Four And Six Dimensions, in Topology, geometry and quantum field theory. Proceedings, Symposium in the honour of the 60th birthday of Graeme Segal, Oxford, U.K., 24–29 June 2002, pp. 405–419 (2007) [arXiv:0712.0157] [INSPIRE].
H. Elvang and T.M. Olson, RG flows in d dimensions, the dilaton effective action and the a-theorem, JHEP03 (2013) 034 [arXiv:1209.3424] [INSPIRE].
M. Movshev and A. Schwarz, Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories, JHEP09 (2012) 136 [arXiv:0910.0620] [INSPIRE].
G. Bossard, P.S. Howe, U. Lindström, K.S. Stelle and L. Wulff, Integral invariants in maximally supersymmetric Yang-Mills theories, JHEP05 (2011) 021 [arXiv:1012.3142] [INSPIRE].
C.-M. Chang, Y.-H. Lin, Y. Wang and X. Yin, Deformations with Maximal Supersymmetries Part 1: On-shell Formulation, arXiv:1403.0545 [INSPIRE].
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge University Press (2007) [INSPIRE].
E.A. Bergshoeff, A. Bilal, M. de Roo and A. Sevrin, Supersymmetric nonAbelian Born-Infeld revisited, JHEP07 (2001) 029 [hep-th/0105274] [INSPIRE].
Z. Bern, J.J. Carrasco, L.J. Dixon, M.R. Douglas, M. von Hippel and H. Johansson, D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops, Phys. Rev.D 87 (2013) 025018 [arXiv:1210.7709] [INSPIRE].
R. Slansky, Group Theory for Unified Model Building, Phys. Rept.79 (1981) 1 [INSPIRE].