Large $N$ matrix models for 3d ${\cal N}=2$ theories: twisted index, free energy and black holes - INSPIRE

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Large $N$ matrix models for 3d ${\cal N}=2$ theories: twisted index, free energy and black holes

Seyed Morteza Hosseini
(
- INFN, Milan Bicocca and
- Milan Bicocca U.
)
,
Alberto Zaffaroni
(
- INFN, Milan Bicocca and
- Milan Bicocca U.
)

Apr 11, 2016

40 pages

Published in:

JHEP 08 (2016) 064

Published: Aug 9, 2016

e-Print:

1604.03122 [hep-th]

DOI:

10.1007/JHEP08(2016)064

View in:

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Abstract: (Springer)

We provide general formulae for the topologically twisted index of a general three-dimensional

\mathcal{N}

≥ 2 gauge theory with an M-theory or massive type IIA dual in the large N limit. The index is defined as the supersymmetric path integral of the theory on S

^{2}

× S

^{1}

in the presence of background magnetic fluxes for the R- and global symmetries and it is conjectured to reproduce the entropy of magnetically charged static BPS AdS

_{4}

black holes. For a class of theories with an M-theory dual, we show that the logarithm of the index scales indeed as N

^{3/2}

(and N

^{5/3}

in the massive type IIA case). We find an intriguing relation with the (apparently unrelated) large N limit of the partition function on S

^{3}

. We also provide a universal formula for extracting the index from the large N partition function on S

^{3}

and its derivatives and point out its analogy with the attractor mechanism for AdS black holes.

Note:

39 pages; v2: refs added; v3: typos removed

AdS-CFT Correspondence
Black Holes in String Theory
M-Theory
black hole: anti-de Sitter
M-theory: duality
partition function
twist
supersymmetry: 2
matrix model
free energy

References(53)

Figures(0)

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