Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories

By Cyril Closset, T. Dumitrescu, G. Festuccia, Z. Komargodski, N. Seiberg. 2012

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A bstractWe consider three-dimensional $ \mathcal{N}=2 $ superconformal field theories on a threesphere and analyze their free energy F as a function of background gauge and supergravity fields. A crucial role is played by certain local terms in these background fields, including several Chern-Simons terms. The presence of these terms clarifies a number of subtle properties of F . This understanding allows us to prove the F -maximization principle. It also explains why computing F via localization leads to a complex answer, even though we expect it to be real in unitary theories. We discuss several corollaries of our results and comment on the relation to the F -theorem.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/49a53ce30e78f1ea000d219e837ad956a8a7d61a

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Citations in the corpus

Supersymmetry on curved spaces and holography (2012, background): “As for the analogue of a-maximisation, Jafferis proposed that F itself is the right function which determines the exact R-symmetry via extremisation [14], and in [137] it has been argued that it is actually maximised.”
The geometry of supersymmetric partition functions (2013, background): “The corresponding supergravity theory was recently studied in superspace [19-21], as well as in components [3,4,16].”
Interpolating between a and F (2014, methodology): “be applied to any Wess-Zumino type model with four supercharges on Sd, 2 d4. As we will show below, our proposal smoothly interpolates between the a-maximization [7] in d= 4, and the F-maximization [11,18,20] in d= 3. We start by observing that the function (5.8) appearing in the 3d localization for”
Supersymmetric field theories on three-manifolds (2012, methodology): “(The two-point functions of flavor currents can be extracted from the partition function on a round three-sphere [33].”
Sphere partition functions and the Zamolodchikov metric (2014, unknown): “See, for example, the discussions in [8,9,10].”
Exact results for the entanglement entropy and the energy radiated by a quark (2013, background): “It was shown in [46] that it arises from a local counterterm because the regularization that is implicitly used in performing the localization procedure does not respect the unitarity of the theory.”
Exact Kähler potential from gauge theory and mirror symmetry (2012, background): “In [16] the authors have pointed out that superconformality and unitarity are not respected in the framework of the exact three-sphere partition function [17, 18, 19] due to unitarity violating terms inevitable when putting rigid supersymmetric theories on a curved manifold, even though the theories”
Two-dimensional SCFTs from wrapped branes and c-extremization (2013, methodology): “After having established a-maximization in four dimensions [8], F -maximization in three dimensions [9, 10] and c-extremization in two dimensions [1], it is natural to wonder whether a similar principle exists in other dimensions.”
Black hole microstates in AdS4 from supersymmetric localization (2015, methodology): “es: a-maximization works in four dimensions [22,23] and c-extremization in two [16]. In odd dimensions, we have so far the example of three dimensions where the partition function on S3 is extremized [21,24,25]. The natural candidate for an extremization in one dimension is the partition function on”
Mutual information and the F-theorem (2015, background): “(3)See also [26, 27] for discussion from the perspective of the free energy.”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, background): “However x is complexified because of the R-symmetry, and the actual contribution to the partition function is exp [ i 2 ( x+ i(R−1) )2] , accounting for extra CS terms including the R-symmetry, whose physical origin has been recently explained in [41] for theories on S(3).”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “In principle, any such ambiguity should be accounted for by an appropriate supersymmetric counterterm [52, 44] but the precise mechanism in this case is unclear to us at this point.”