Rigid supersymmetric theories in curved superspace

By G. Festuccia, N. Seiberg. 2011

718 citations recorded by the source corpus.

We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $ \mathcal{M} $, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For $ \mathcal{M} = Ad{S_4} $ we reproduce the known results in the literature. A supersymmetric Lagrangian for $ \mathcal{M} = {\mathbb{S}^4} $ exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for $ \mathcal{M} = {\mathbb{S}^3} \times \mathbb{R} $ and note that the time direction $ \mathbb{R} $ can be rotated to Euclidean signature and be compactified to $ {\mathbb{S}^1} $ only when the theory has a continuous R-symmetry. The partition function on $ \mathcal{M} = {\mathbb{S}^3} \times {\mathbb{S}^1} $ is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant $ \mathcal{N} = 2 $ theories on $ {\mathbb{S}^3} $ and clarify a few points about them.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/99b5a196777c704af8f2f355d66f1cc1c4c80536

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Citations in the corpus

Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “For certain expectation values of the fields inH, the theory also preserves some amount of rigid supersymmetry [27].”
F-theorem without supersymmetry (2011, background): “These ideas have passed some field theoretic tests [18,29–38], and various issues in defining supersymmetric theories on S(3) were clarified in [39].”
Correlation functions of Coulomb branch operators (2016, background): “1) by specific 1/r and 1/r(2) terms, where r is the radius of S(4), as in [46].”
Localization techniques in quantum field theories (2016, methodology): “Our present discussion can be summarized in the following table: dim multiplet #super special function references derivation S2 N = 2 vector 4 Υ1(x| ) [36,37] Chapter 3 S3 N = 2 vector 4 S2(x| ) [35] Chapter 6 S4 N = 2 vector 8 Υ2(x| ) [16] Chapter 10 S5 N = 1 vector 8 S3(x| ) [38–40] Chapter 14 S6 ”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “The quasi-topological twisting that we use in this paper is best understood in the context of curved-space rigid supersymmetry [85, 86].”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, background): “Indeed, the relation between rigid and local supersymmetry is already clear from the results of [12].”
Exact Kähler potential from gauge theory and mirror symmetry (2012, background): “19) are precisely those of the theory in flat space, even though the action of a supersymmetric theory on curved space is generically corrected by 1/r terms [14].”
Two-Sphere Partition Functions and Gromov–Witten Invariants (2012, neutral): “This requires a deformation of the Lagrangian of the theory by terms of order 1 R and 1 R2 (see [48] for a general discussion) and, correspondingly, the theory on S2 obeys a deformed supersymmetry algebra with variational parameters given by conformal Killing spinors of S2.”
The geometry of supersymmetric partition functions (2013, methodology): “Following [40–42], who studied partition functions of three-dimensional N = 2 theories with a U(1)R symmetry on round spheres preserving four supercharges, much recent work has focused on squashed spheres [43–51], i.e. three-manifolds that are diffeomorphic to S3 but carry a more general metric with”
Supersymmetric field theories on three-manifolds (2012, methodology): “As in four dimensions [30], we can choose Aμ = Vμ and compactify R to S(1).”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, background): “For a recent discussion on related issues in three and four dimensions one may consult [29, 30, 31].”
Comments on 3d Seiberg-like dualities (2011, background): “On the other hand, the supersymmetric gauging of the R-symmetry is more subtle; see [26, 21, 27] for recent discussions.”
Top down approach to 6D SCFTs (2018, background): “on to preserve symmetry on this background follows from an analysis of the o-shell structure of minimal 6D supergravity which would in principle follow from an extension of the analysis in reference [193] though as far as we are aware this has only been carried out for some limited examples [194]. E”
Sphere partition functions and the Zamolodchikov metric (2014, background): “Manifolds that preserve four supercharges obey the integrability conditions [16]:”
Bootstrapping the superconformal index with surface defects (2012, background): “1 In several cases (1)More general susy-preserving backgrounds are beginning to be explored [1, 2].”
Seiberg-Witten theories on ellipsoids (2012, methodology): “Some systematic analysis has been made in [12, 13, 14, 15, 16] to draw conditions on the background geometry from Killing spinor equation.”