arXiv subjects

Christopher Couzens

Publications and source records attributed to Christopher Couzens.

27 records · Page 2Linked to original sources

arXiv2020

The Near-Horizon Geometry of Supersymmetric Rotating AdS$_4$ Black Holes in M-theory

We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity. Such rotating black holes admit an AdS$_2$ near-horizon geometry which is fibered by the transverse spacetime directions. Despite their clear interest to understanding the entropy of rotating black holes, these solutions have evaded all previous supersymmetric classification programs due to the non-trivial fibration structure. In this paper we allow for the most general fibration over AdS$_2$ with a flux configuration permitting rotating M2-branes. Using G-structure techniques we rewrite the conditions for supersymmetry in terms of differential equations on an eight-dimensional balanced space. The 9d compact internal space is a U$(1)$-fibration over this 8d base. The geometry is constrained by a master equation reminiscent of the one found in the non-rotating case. We give a Lagrangian from which the equations of motion may be derived, and show how the asymptotically AdS$_4$ electrically charged Kerr-Newman black hole in 4d $\mathcal{N}=2$ supergravity is embedded in the classification. In addition, we present the conditions for the near-horizon geometry of rotating black strings in Type IIB by using dualities with the 11d setup.

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arXiv2020

Anomalies of (0,4) SCFTs from F-theory

We study the macroscopics of 2d $\mathcal{N}=(0,4)$ SCFTs arising from F-theory constructions. The class of 2d SCFTs we consider live on black strings which are obtained by wrapping D3-branes on a curve in the base of a possibly singular elliptically fibered Calabi-Yau threefold. In addition, we allow the D3-branes to probe ALE or ALF spaces transversely. We compute anomaly coefficients of these SCFTs by determining Chern-Simons terms in the 3d action resulting from the reduction of 6d $\mathcal{N}=(1,0)$ supergravity on the compact space surrounding the black string. Essential contributions to these coefficients are from one-loop induced Chern-Simons terms arising from integrating out massive Kaluza-Klein modes.

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arXiv2019

Twisted $\mathcal{N}=1$ SCFTs and their AdS$_3$ duals

We study compactifications of an infinite family of four-dimensional $\mathcal{N}=1$ SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting two-dimensional $\mathcal{N}=(0,2)$ theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS$_3$ duals of two-dimensional field theories.

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arXiv2019

$\mathcal{N}=(0,2)$ AdS$_3$ Solutions of Type IIB and F-theory with Generic Fluxes

We consider the most general AdS$_3$ solutions of type IIB supergravity admitting a dynamical SU$(3)$ structure and preserving $\mathcal{N}=(0,2)$ supersymmetry. The analysis is broken into three distinct classes depending on whether the dynamical SU$(3)$ structure degenerates to a strict SU$(3)$ structure. The first class we consider allows for a holomorphically varying axio-dilaton consistent with the presence of $(p,q)$ 7-branes in addition to D3-branes and $(p,q)$ 5-branes. In the remaining two classes the axio-dilaton may vary but does not do so holomorphically. The second class of solution allows for 5-branes and 1-branes but no D3-branes, whilst in the final class all branes can be present. We illustrate our results with examples of such solutions including a new infinite family with all fluxes but the axion turned on.

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arXiv2019

Black Holes and (0,4) SCFTs from Type IIB on K3

We study the central charges and levels of 2d $\mathcal{N}=(0,4)$ superconformal field theories that are dual to four- and five-dimensional BPS black holes in compactifications of type IIB string theory on a K3 surface. They arise from wrapping a D3-brane on a curve $C$ inside K3 and have transverse space either an ALE or ALF space. These D3-branes have an AdS$_3 \times \mathrm{S}^3/ Γ$ near horizon geometry where $Γ$ is a discrete subgroup of $SU(2)$. We compute the central charges and levels of the 2d SCFTs both in the microscopic picture and from six-dimensional $\mathcal{N}=(2,0)$ supergravity. These quantities determine the black hole entropy via Cardy's formula. We find agreement between the microscopic and macroscopic computations. The contributions from one-loop quantum corrections to the macroscopic result are crucial for this matching.

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arXiv2019

A geometric dual of $c$-extremization

We consider supersymmetric AdS$_3 \times Y_7$ and AdS$_2 \times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively, that are holographically dual to SCFTs with $(0,2)$ supersymmetry in two dimensions and $\mathcal{N}=2$ supersymmetry in one dimension. The geometry of $Y_{2n+1}$, which can be defined for $n\ge 3$, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for $n=3$ one can compute the central charge of an AdS$_3 \times Y_7$ solution without knowing its explicit form. We interpret this as a geometric dual of $c$-extremization in $(0,2)$ SCFTs. For the case of AdS$_2 \times Y_9$ solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS$_4$. We also study many specific examples of the type AdS$_3\times T^2 \times Y_5$, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the $(0,2)$ SCFTs dual to these solutions can arise from the compactification on $T^2$ of certain $d=4$ quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion.

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arXiv2018

F-theory and AdS_3/CFT_2 (2,0)

We continue to develop the program initiated in arXiv:1705.04679 of studying supersymmetric AdS_3 solutions of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of 4d theories with varying coupling. Imposing 2d N=(0,2) supersymmetry, we derive the general conditions on the geometry for Type IIB AdS_3 solutions with varying axio-dilaton and five-form flux. We discuss a class of solutions, which extend AdS_3 x T^2 x M_5 Type IIB backgrounds, to F-theory geometries of the type AdS_3 x K3 x M_5 with varying axio-dilaton characterizing the elliptic fiber of the K3, and describe their dual field theories. For a specific choice of M_5 this corresponds to a family of solutions that are conjectured to be dual to twisted compactifications of 4d N=1 Y^{p,q} quiver gauge theories on a curve with varying coupling. For this setup, we compare the central charges from holography and field theory and find agreement to subleading order in N. Requiring enhanced 2d N=(2,2) supersymmetry we find that the axio-dilaton must be constant. However, if the internal geometry is allowed to be non-compact, we obtain the most general class of Type IIB AdS_5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.

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arXiv2017

F-theory and AdS_3/CFT_2

We construct supersymmetric AdS_3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d N=(0,4) superconformal field theories with small superconformal algebra. In F-theory these arise from D3-branes wrapped on curves in the base of an elliptically fibered Calabi-Yau threefold Y_3 and correspond to strings in the 6d N=(1,0) theory obtained from F-theory on Y_3. The non-trivial fibration over the wrapped curves implies a varying coupling of the N=4 Super-Yang-Mills theory on the D3-branes. We compute the holographic central charges and show that these agree with the field theory and with the anomalies of self-dual strings in 6d. We complement our analysis with a discussion of the dual M-theory solutions and a comparison of the central charges.

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arXiv2016

Supersymmetric AdS$_{5}$ solutions of type IIB supergravity without D3 branes

We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space (AdS$_5$) with a five-dimensional Riemannian manifold $M_{5}$, where the five-form flux vanishes, while all remaining fluxes are allowed to be non-vanishing consistent with SO(4,2) symmetry. This completes the program of classifying all supersymmetric solutions of ten and eleven-dimensional supergravity with an AdS$_5$ factor. We investigate the supersymmetry conditions in some special cases, and demonstrate how these are satisfied by a solution originally found in arXiv:1410.2650[hep-th], utilising the method of non-Abelian T-duality.

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