The free energy of $ \mathcal{N} = 2 $ supersymmetric AdS4 solutions of M-theory

Abstract:We compute the quantum gravity partition function of M-theory on AdS 4 ×X 7 by using localization techniques in four-dimensional gauged supergravity obtained by a consistent truncation on the Sasaki-Einstein manifold X 7 . The supergravity path integral reduces to a finite dimensional integral over two collective coordinates that parametrize the localizing instanton solutions. The renormalized action of the off-shell instanton solutions depends linearly and holomorphically on the "square root" prepotential evaluated at the center of AdS 4 . The partition function resembles the Laplace transform of the wave function of a topological string and with an assumption about the measure for the localization integral yields an Airy function in precise agreement with the computation from the boundary ABJM theory on a 3-sphere. Our bulk quantum gravity computation is nonperturbatively exact in four-dimensional Planck length but ignores corrections due to brane-instantons.

Section: Localization In the Boundary Gauge Theory And The Airy Functionmentioning

confidence: 63%

Localization in supergravity and quantum AdS 4 /CFT3 holography

Dabholkar

Drukker

Gomes

2014

“…A contact form η always has an associated unique Reeb vector field ξ, defined via the equations ξ η = 1, ξ dη = 0, and in [24,25] it was shown that ξ is also the R-symmetry Killing vector field, 2 Similar Wilson loops have recently been considered in five-dimensional superconformal field theories on S 5 [43], which may also be computed using localization techniques. The gravity duals are described by warped AdS6 × S 4 /Zn solutions of massive IIA supergravity, and thus the geometry of the internal spaces here is fixed and in fact unique [44].…”

Section: Jhep01(2014)083mentioning

confidence: 99%

“…Since (1.4) depends only on η we may compute this expression in examples using the same methods employed in [24,25,45]- [49]. For example, for toric solutions (1.4) may be computed entirely using toric geometry methods.…”

Section: Jhep01(2014)083mentioning

confidence: 99%

“…Our starting point is to consider BPS M2-branes in general N = 2 supersymmetric AdS 4 ×Y 7 solutions of eleven-dimensional supergravity. These backgrounds were studied in detail in [24,25], where it was shown that provided the quantized M2-brane charge N of the background (measured by a certain flux integral) is non-zero, then there is always a canonical contact one-form η defined on Y 7 . Concretely, η is constructed as a bilinear in the Killing spinors on Y 7 , and it was shown in the latter reference that this contact structure entirely captures both the gravitational free energy of the background, and also the scaling dimensions of BPS operators arising from supersymmetric M5-branes wrapped on five-manifolds Σ 5 ⊂ Y 7 .…”

Section: Jhep01(2014)083mentioning

confidence: 99%

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Wilson loops and the geometry of matrix models in AdS4/CFT3

Farquet

Sparks

2014

Self Cite

We study a general class of supersymmetric AdS 4 × Y 7 solutions of M-theory that have large N dual descriptions as N = 2 Chern-Simons-matter theories on S 3 . The Hamiltonian function h M for the M-theory circle, with respect to a certain contact structure on Y 7 , plays an important role in the duality. We show that an M2-brane wrapping the M-theory circle, giving a fundamental string in AdS 4 , is supersymmetric precisely at the critical points of h M , and moreover the value of this function at the critical point determines the M2-brane action. Such a configuration determines the holographic dual of a BPS Wilson loop for a Hopf circle in S 3 , and leads to an effective method for computing the Wilson loop on both sides of the correspondence in large classes of examples. We find agreement in all cases, including for several infinite families, and moreover we find that the image h M (Y 7 ) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h M mapping to points where the derivative of the eigenvalue density is discontinuous.

“…To calculate the free energy, we evaluate the action (3.1) of the solution (3.2) with the boundary and counter terms [24,25] …”

Section: Jhep07(2014)061mentioning

confidence: 99%

The gravity dual of supersymmetric Rényi entropy

Nishioka

2014

Supersymmetric Rényi entropies are defined for three-dimensional N = 2 superconformal field theories on a branched covering of a three-sphere by using the localized partition functions. Under a conformal transformation, the branched covering is mapped to S 1 × H 2 , whose gravity dual is the charged topological AdS 4 black hole. The black hole can be embedded into four-dimensional N = 2 gauged supergravity where the mass and charge are related so that it preserves half of the supersymmetries. We compute the supersymmetric Rényi entropies with and without a certain type of Wilson loop operators in the gravity theory. We find they agree with those of the dual field theories in the large-N limit.