The gravity dual of supersymmetric gauge theories on a squashed S 1 × S 3

Martelli, Dario

doi:10.1007/jhep08(2014)044

Cited by 37 publications

(138 citation statements)

References 69 publications

(237 reference statements)

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“…Since the supersymmetric Casimir energy has an N 2 (in 4d) or N 3 (in 6d) scaling with the rank of the gauge group it is natural to expect that it should be also accessible by a holographic calculation. This was already discussed to some extent in [2,8] in four dimensions, but the precise holographic interpretation is not yet clear and deserves further study. It is tantalizing to speculate that there might be a connection between the supersymmetric Casimir energy for N = 4 SYM computed in section 4 above and some physical quantity for the Gutowski-Reall black hole [78,79] and its generalizations [80,81].…”

Section: Jhep09(2015)142mentioning

confidence: 89%

“…This result was further clarified in [2,7] where it was shown that there are no finite counterterms and E is scheme-independent. The relation (1.3) was further studied in [8] where the authors discussed a holographic interpretation of this result. 1 We refer to the quantity E and its cousins for SCFTs in other even dimensions as the supersymmetric Casimir energy.…”

Section: Introductionmentioning

confidence: 95%

“…With these assumptions, the Lagrangians for the chiral and the Fermi multiplets are given by (see for example [52]) 8) while the vector multiplet Lagrangian is…”

Section: Jhep09(2015)142mentioning

confidence: 99%

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Supersymmetric Casimir energy and the anomaly polynomial

Bobev

Bullimore

Kim

2015

J. High Energ. Phys.

108

207

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We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D−1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

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Section: Jhep09(2015)142mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 95%

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Supersymmetric Casimir energy and the anomaly polynomial

Bobev

Bullimore

Kim

2015

J. High Energ. Phys.

108

207

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“…On general grounds, we expect that they differ by local counter-terms and by Casimir energy factors (Casimir energy factors are indeed present, see for example [39,40]). Both of these effects necessarily scale like O(β), therefore they are inconsequential as far as the singular terms in β go.…”

Section: Hopf Surfacesmentioning

confidence: 99%

Cardy formulae for SUSY theories in d = 4 and d = 6

Pietro

Komargodski

2014

J. High Energ. Phys.

160

358

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We consider supersymmetric theories on a space with compact space-like slices. One can count BPS representations weighted by (−1) F , or, equivalently, study supersymmetric partition functions by compactifying the time direction. A special case of this general construction corresponds to the counting of short representations of the superconformal group. We show that in four-dimensional N = 1 theories the "high temperature" asymptotics of such counting problems is fixed by the anomalies of the theory. Notably, the combination a − c of the trace anomalies plays a crucial role. We also propose similar formulae for six-dimensional (1, 0) theories.

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“…The holographic energy-momentum tensor T ij and R-symmetry current j i may be computed with standard formulas (see e.g. [7]). The former is particularly unwieldy, but we have verified that these satisfy the expected Ward identities.…”

Section: Dual Supergravity Solutionsmentioning

confidence: 99%

The holographic supersymmetric Casimir energy

et al. 2017

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We consider a general class of asymptotically locally AdS5 solutions of minimal gauged supergravity, which are dual to superconformal field theories on curved backgrounds S 1 × M3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S 1 × R 4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges. I. THE SUPERSYMMETRIC CASIMIR ENERGYIn [1, 2] a new observable of d = 4 superconformal field theories has been introduced: the supersymmetric Casimir energy. This is defined by putting the theory on certain curved backgrounds M 4 = S 1 β × M 3 , where S 1 β is a circle of length β and M 3 is a compact threemanifold. These are rigid supersymmetric backgrounds, and the supersymmetric Casimir energy is defined asHere the partition function Z susy is computed with periodic boundary conditions for the fermions around S 1 β . A key point is that, unlike the vacuum energy of general d = 4 conformal field theories (CFTs), E susy is schemeindependent and thus an intrinsic observable.The rigid supersymmetric backgrounds of interest comprise a metric on M 4 of the formwhere τ ∼ τ + β is a coordinate on S 1 β . The vector ∂ ψ is Killing, and generates a transversely holomorphic foliation of M 3 , with local transverse complex coordinate z. The local one-form a satisfies da = iu e w dz ∧ dz, where w = w(z,z), u = u(z,z). In addition there is a non-dynamical Abelian gauge field, which couples to the R-symmetry current and arises when the field theory is coupled to background conformal supergravity, given byNotice that the second line is locally pure gauge; however, the constant γ will play an important role. The background geometry thus depends on the choice of the two functions w(z,z), u(z,z), and via (1) the supersymmetric Casimir energy also a priori depends on this choice. These backgrounds admit two supercharges of opposite R-charge, and associated to each of these is an integrable complex structure (i.e. they are ambiHermitian). In [3] it is argued that the supersymmetric partition function depends on the background only via the choice of complex structure(s). In the present set-up, this implies that Z susy depends only on the transversely holomorphic foliation generated by ∂ ψ . In particular, deformations of w(z,z) and u(z,z) that leave this foliation fixed should not change E susy .Later in this paper we will focus on the case that topologically M 3 ∼ = S 3 . Here we may embed S 3 ⊂ R 4 = R 2 ⊕ R 2 , and write, where ϕ 1 , ϕ 2 are standard 2π periodic azimuthal angles. In this case the above statements imply that E susy should depend only on b 1 , b 2 , and the explicit calculation in [1] givesHere a and c are the usual trace anomaly coefficients for a d = 4 CFT. For field theories admitting a large N gravity dual in type IIB supergravity, to leading order in the ...

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The gravity dual of supersymmetric gauge theories on a squashed S 1 × S 3

Cited by 37 publications

References 69 publications

Supersymmetric Casimir energy and the anomaly polynomial

Supersymmetric Casimir energy and the anomaly polynomial

Cardy formulae for SUSY theories in d = 4 and d = 6

The holographic supersymmetric Casimir energy

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