Abstract
We study the holographic dual to cc-extremization for 2d (0,2)(0,2) superconformal field theories (SCFTs) that have an AdS_33 dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS_33 solutions can be mapped to AdS_22 solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic cc-extremization in F-theory and \mathcal{I}ℐ-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.
Highlights
A Type IIB supergravity solution with a holomorphically varying axio-dilaton can be given an F-theory interpretation, whereby the varying axio-dilaton is represented as the complex structure of a singular elliptic fibration over spacetime
From the point of view of the 4d N = 4 Super-Yang-Mills (SYM) theory on the D3-branes, this corresponds to a varying complexified coupling, and the 2d superconformal field theories (SCFTs) is obtained by a duality-twist [13,14,15,16]
We develop the holographic dual to c-extremization in the context of AdS3 geometries in Ftheory, i.e. Type IIB supergravity with a holomorphically varying axio-dilaton τ, which are holographically dual to 2d N = (0, 2) SCFTs
Summary
A Type IIB supergravity solution with a holomorphically varying axio-dilaton can be given an F-theory interpretation, whereby the varying axio-dilaton is represented as the complex structure of a singular elliptic fibration over spacetime. Whether one takes the geometric or field theoretic point of view, the extremization principles generally represent a significant simplification of the problem of determining genuine supergravity backgrounds or, equivalently, their dual SCFTs. Instead of directly having to solve a set of coupled (partial) differential equations, we can take the much more technically tractable approach of optimizing a single function. In this paper we generalize this approach to include a varying axio-dilaton, which provides a powerful tool for identifying F-theory AdS3 supergravity solutions that can arise from configurations of D3-branes and 7-branes From this point of view the duality with M-theory AdS2 backgrounds provides a description where the elliptic fibration associated with the varying axio-dilaton is physically manifest, it implies that in this specific context holographic I- and c-extremization are dual to each other.
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