The Casimir energy in curved space and its supersymmetric counterpart

We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an SL(3, Z) transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for N = 1 SQCD and N = 4 supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally. We also use our method to derive an expression for the Casimir energy of the nonlagrangian N = 2 SCFT with E 6 flavour symmetry. Furthermore, we predict an expression for Casimir energy of the N = 1 SP(2N) theory with SU(8) × U(1) flavour symmetry that is part of a multiple duality network, and for the doubled N = 1 theory with enhanced E 7 flavour symmetry.

Section: Discussionmentioning

confidence: 99%

Section: Jhep07(2017)041mentioning

confidence: 99%

Section: Mapping Hopf Surfaces and Asymptoticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Supersymmetric Casimir energy and S L 3 ℤ $$ \mathrm{S}\mathrm{L}\left(3,\mathrm{\mathbb{Z}}\right) $$ transformations

Brünner

Regalado

Spiridonov

2017

“…The resulting partition functions, up to a Casimir energy factor [5][6][7][8], count the states in the Hilbert space of the theory on M d−1 that are annihilated by {Q,Q}, weighted by the fermion number (−1) F . From the index interpretation it follows that they are independent on continuous coupling constants [9], therefore their computation at weak coupling is valid even when the coupling is large.…”

Section: Introductionmentioning

confidence: 99%

Cardy formula for 4d SUSY theories and localization

Pietro

Honda

2017

Self Cite

119

Abstract:We study 4d N = 1 supersymmetric theories on a compact Euclidean manifold of the form S 1 × M 3 . Partition functions of gauge theories on this background can be computed using localization, and explicit formulas have been derived for different choices of the compact manifold M 3 . Taking the limit of shrinking S 1 , we present a general formula for the limit of the localization integrand, derived by simple effective theory considerations, generalizing the result of [1]. The limit is given in terms of an effective potential for the holonomies around the S 1 , whose minima determine the asymptotic behavior of the partition function. If the potential is minimized in the origin, where it vanishes, the partition function has a Cardy-like behavior fixed by Tr(R), while a nontrivial minimum gives a shift in the coefficient. In all the examples that we consider, the origin is a minimum if Tr(R) ≤ 0.

Conformal anomaly c-coefficients of superconformal 6d theories

Beccaria

Tseytlin

2016

We propose general relations between the conformal anomaly and the chiral (R-symmetry and gravitational) anomaly coefficients in 6d (1, 0) superconformal theories. The suggested expressions for the three type B conformal anomaly ci-coefficients complement the expression for the type A anomaly a-coefficient found in arXiv:1506.03807. We check them on several examples — the standard (1, 0) hyper and tensor multiplets as well as some higher derivative short multiplets containing vector fields that generalize the super-conformal 6d vector multiplet discussed in arXiv:1506.08727. We also consider a family of higher derivative superconformal (2, 0) 6d multiplets associated to 7d multiplets in the KK spectrum of 11d supergravity compactified on S4. In particular, we prove that (2,0) 6d conformal supergravity coupled to 26 tensor multiplets is free of all chiral and conformal anomalies. We discuss some interacting (1, 0) superconformal theories, predicting the ci-coefficients for the “E-string” theory on multiple M5-branes at E8 9-brane and for the theory describing M5-branes at an orbifold singularity C2/ΓC2/Γ . Finally, we elaborate on holographic computation of subleading corrections to conformal anomaly coefficients coming from R2 + R3 terms in 7d effective action, revisiting, in particular, the (2,0) theory case