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The topologically twisted index of \( \mathcal{N} \) = 4 super-Yang-Mills on T 2 × S2 and the elliptic genus

Abstract We examine the topologically twisted index of \( \mathcal{N} \) = 4 super-Yang-Mills with gauge group SU(N ) on T 2×S2, and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds T2/ℤm × ℤn where N = mn. After summing over these sectors, the index can be expressed as the elliptic genus of a twodimensional \( \mathcal...

Comments on higher rank Wilson loops in \( \mathcal{N} \) = 2∗

For \( \mathcal{N} \) = 2∗ theory with U(N ) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigen-value distributions in various...

Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity

The topologically twisted index for ABJM theory with gauge group U(N) k × U(N)−k has recently been shown, in the large-N limit, to reproduce the BekensteinHawking entropy of certain magnetically charged asymptotically AdS4 black holes. We numerically study the index beyond the large-N limit and provide evidence that it contains a subleading logarithmic term of the form −1/2 log N...

One-loop supergravity on AdS4 × S 7/ℤ k and comparison with ABJM theory

The large-N limit of ABJM theory is holographically dual to M-theory on AdS4 × S 7/ℤ k . The 3-sphere partition function has been obtained via localization, and its leading behavior F ABJM (0) ∼ k 1/2 N 3/2 is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading \( \mathcal{O}\left({N}^0\right) \) order by computing the...

Holographic Lifshitz fermions and exponentially suppressed spectral weight

The absence of fixed momentum excitations in a theory with Lifshitz scale invariance gives rise to exponential suppression of spectral weight in the low-frequency limit. In the holographic dual, this suppression arises as a consequence of a tunneling barrier that decouples the horizon from the boundary. We compute the spin-1/2 holographic Green’s function and show that the form...

Rigid supersymmetric backgrounds of 3-dimensional Newton-Cartan supergravity

Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the c → ∞ limit of three dimensional \( \mathcal{N} \) = 2 super-gravity [1]. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all...

A holographic c-theorem for Schrödinger spacetimes

We prove a c-theorem for holographic renormalization group flows in a Schrödinger spacetime that demonstrates that the effective radius L(r) monotonically decreases from the UV to the IR, where r is the bulk radial coordinate. This result assumes that the bulk matter satisfies the null energy condition, but holds regardless of the value of the critical exponent z. We also...

Higher rank ABJM Wilson loops from matrix models

We compute the vacuum expectation values of 1/6 supersymmetric Wilson loops in higher dimensional representations of the gauge group in ABJM theory. We present results for the m-symmetric and m-antisymmetric representations by exploiting standard matrix model techniques. At leading order, in the saddle point approximation, our expressions reproduce holographic results from both...

Universal features of Lifshitz Green’s functions from holography

We examine the behavior of the retarded Green’s function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green’s function is fixed (up to normalization) by symmetry, the generic Lifshitz Green’s function can a priori depend on an arbitrary function...

High-temperature expansion of supersymmetric partition functions

Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy’s formula, which gives the leading high-temperature (β → 0) behavior of supersymmetric partition functions Z SUSY(β). Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular...

Hidden horizons in non-relativistic AdS/CFT

Cynthia Keeler 0 Gino Knodel 0 James T. Liu 0 0 Michigan Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan , Ann Arbor, MI 48109-1040, U.S.A We study

On \( \mathcal{N}=1 \) partition functions without R-symmetry

We examine the dependence of four-dimensional Euclidean \( \mathcal{N}=1 \) partition functions on coupling constants. In particular, we focus on backgrounds without R-symmetry, which arise in the rigid limit of old minimal supergravity. Backgrounds preserving a single supercharge may be classified as having either trivial or SU(2) structure, with the former including S 4. We...

c − a from the \( \mathcal{N}=1 \) superconformal index

We present a prescription for obtaining the difference of the central charges, c−a, of a four dimensional superconformal quantum field theory from its single-trace index. The formula is derived from a one-loop holographic computation, but is expected to be valid independent of holography. We demonstrate the prescription with several holographic and non-holographic examples. As an...

What do non-relativistic CFTs tell us about Lifshitz spacetimes?

Cynthia Keeler 0 Gino Knodel 0 James T. Liu 0 0 Michigan Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan , Ann Arbor, MI 48109-1040, U.S.A We study the

Small treatise on spin-3/2 fields and their dual spectral functions

In this work we systematically study various aspects of spin-3/2 fields in a curved background. We mostly focus on a minimally coupled massive spin-3/2 field in arbitrary dimensions, and solve the equation of motion either explicitly or numerically in AdS, Schwarzschild-AdS and Reissner-Nordström-AdS backgrounds. Although not the main focus of this work, we also make a connection...

The shortened KK spectrum of IIB supergravity on Y p,q

Arash Arabi Ardehali 1 James T. Liu 1 Phillip Szepietowski 0 Open Access c The Authors. Article funded by SCOAP 0 Department of Physics, University of Virginia , Box 400714, Charlottesville, VA

1/N 2 corrections to the holographic Weyl anomaly

We compute the \( \mathcal{O} \) (1) contribution to holographic c − a for IIB supergravity on AdS5 × S 5 / \( {{\mathbb{Z}}_n} \) and on AdS5 × T 1,1 / \( {{\mathbb{Z}}_n} \) . In both cases, we find agreement with the dual field theory results, thus providing 1/N 2 checks of AdS/CFT with reduced supersymmetry. Since the holographic computation involves a sum over shortened...

On \(\mathcal{N} = 2\) truncations of IIB on T 1,1

We study the \(\mathcal{N} = 4\) gauged supergravity theory which arises from the consistent truncation of IIB supergravity on the coset T 1,1. We analyze three \(\mathcal{N} = 2\) subsectors and in particular we clarify the relationship between true superpotentials for gauged supergravity and certain fake superpotentials which have been widely used in the literature. We derive a...