On renormalization group flows and the a-theorem in 6d

By Henriette Elvang, D. Freedman, Ling-Yan Hung, Michael Kiermaier, R. Myers, S. Theisen. 2012

164 citations recorded by the source corpus.

A bstractWe study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d = 6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow aUV − aIR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p6 in the low energy limit of n-point scattering amplitudes of the dilaton for n ≥ 4. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS7 × S4.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8506959b74490623b10a0be07114243844157b75

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Citations in the corpus

Beyond the Cosmological Standard Model (2014, unknown): “Here we have only focused on the simplest dispersion relation, it is possible to extract more intricate ones using similar arguments [546, 1022, 1023].”
Top down approach to 6D SCFTs (2018, unknown): “ure is called the \a-theorem," and it was proven by Komargodski and Schwimmer in [154]. In D= 3, there is a related F-theorem [155{157]. In D= 6, however, Cardy’s conjecture remains unproven. In [158], it was shown that the approach of Komargodski and Schwimmer that worked in D= 4 breaks down i”
Anomaly polynomial of general 6D SCFTs (2014, background): “(See [41–45] for some evidences for or against the a-theorem in 6d).”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “See [5] for a discussion of the six-dimensional case.”