A geometric dual of $c$-extremization - INSPIRE

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A geometric dual of $c$ -extremization

Christopher Couzens
(
- Utrecht U.
)
,
Jerome P. Gauntlett
(
- Imperial Coll., London
)
,
Dario Martelli
(
- King's Coll. London, Dept. Math
)
,
James Sparks
(
- Oxford U., Inst. Math. and
- INOA, Florence
)

Oct 25, 2018

67 pages

Published in:

JHEP 01 (2019) 212

Published: Jan 29, 2019

e-Print:

1810.11026 [hep-th]

DOI:

10.1007/JHEP01(2019)212

Report number:

Imperial/TP/2018/JG/03

View in:

reference search74 citations

Citations per year

Abstract: (Springer)

We consider supersymmetric AdS

_{3}

× Y

_{7}

and AdS

_{2}

× 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 ≥ 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}

× 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}

× 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}

× T

^{2}

× 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.

Note:

67 pages. Minor changes, published version

AdS-CFT Correspondence
Differential and Algebraic Geometry
Supersymmetric Gauge Theory
Black Holes in String Theory
vector: Killing
dimension: 2
supergravity: solution
duality: holography
dimension: 1
gauge field theory: quiver

References(66)

Figures(0)

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(
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,
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(
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)
,
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(
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,
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(
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,
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(
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)

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