F-theory and AdS3/CFT2

Journal of High Energy Physics, Aug 2017

We construct supersymmetric AdS3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d \( \mathcal{N}=\left(0,4\right) \) 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 self-dual strings in the 6d \( \mathcal{N}=\left(1,0\right) \) theory obtained from F-theory on Y 3. The non-trivial fibration over the wrapped curves implies a varying coupling of the \( \mathcal{N}=4 \) 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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F-theory and AdS3/CFT2

HJE AdS3/CFT2 Christopher Couzens 0 1 4 Craig Lawrie 0 1 2 Dario Martelli 0 1 4 Sakura Sch¨afer-Nameki 0 1 3 The Strand 0 1 London 0 1 Jin-Mann Wonga 0 Woodstock Road , Oxford, OX2 6GG , U.K 1 Philosophenweg 19 , 69120 Heidelberg , Germany 2 Institut fu ̈r Theoretische Physik, Ruprecht-Karls-Universita ̈t 3 Mathematical Institute, University of Oxford 4 Department of Mathematics, King's College London We construct supersymmetric AdS3 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 Y3 and correspond to self-dual strings in the 6d N = (1, 0) theory obtained from F-theory on Y3. 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. AdS-CFT Correspondence; F-Theory 1 Introduction 2 F-theory and wrapped D3-branes F-theory Elliptic fibrations D3-branes in F-theory and 2d ( 0, 4 ) SCFTs 2.1 2.2 2.3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 4.1 4.2 4.3 5.1 5.2 6.1 6.2 6.3 7.1 7.2 7.3 3 AdS3 solutions in F-theory dual to 2d (0, 4) theories Type IIB Killing spinor equations AdS3 ansatz Constraints for 2d ( 0, 4 ) supersymmetry F-theory AdS3 solution Lens space solution Flux quantisation Brane solutions and the interpretation of the quotient 4 F-theory holographic central charges Leading order central charges cIIB L − cIIB at sub-leading order from anomaly inflow R Level of the superconformal R-symmetry 4.4 Summary: central charges from F-theory 5 M/F-duality and AdS3 solutions in M-theory Dual 11d supergravity solution M5-brane solutions 5.3 Flux quantisation 6 Holographic central charges from M-theory Leading order central charges Chern-Simons terms and c1L1 − c11 R Chern-Simons couplings from 11d supergravity 7 Central charges from anomalies and comparisons Anomalies from M5-branes Anomalies of 6d self-dual strings Anomaly from M5-branes on Cb 7.4 Summary and comparison 8 Conclusions and outlook A Conventions for gamma matrices and spinors – i – C Torsion conditions on spinor bilinears C.1 Simplifying relations C.2 Algebraic equations C.3 Differential conditions: scalars C.4 Differential conditions: one-forms C.5 Differential conditions: higher forms D Supergravity central charges D.1 Holographic central charges at leading order D.2 Holographic central charges at sub-leading order E Properties of K¨ahler and Calabi-Yau varieties E.1 Useful relations E.2 Ample divisors in elliptically fibered Calabi-Yau threefolds F 55 56 far in utilising F-theory has been on the construction and classification of Type IIB vacua with varying axio-dilaton τ , as well as (p, q) 7-branes, which are naturally encoded in the singularities of τ . The canonical setup to construct such vacua is the compactification on elliptic Calabi-Yau varieties Yd of complex dimension d with base Bd−1, where the complex structure of the elliptic fiber models the axio-dilaton. In the current paper we will deviate from this and consider supergravity solutions with AdS vacua of Type IIB supergravity, where we allow the axio-dilaton τ to vary consistently with the SL(2, Z) duality transformations. In this sense we are constructing F-theory solutions. Our main focus will be supersymmetric solutions with AdS factors, which allow for a holographic interpretation. The motivation to study these backgrounds arises from various points of view. It is in general an interesting question to characterise systematically such Type IIB solutions, as a method for exploring superconformal field theories (SCFTs). Moreover, recently1 various D3-brane configurations in F-theory have been shown to give rise to 2d SCFTs [5–9]. These constructions are based on D3-branes wrapped on a complex curve C in the base Bd−1 of the elliptic fibration. Our goal here is to construct holographic duals to such 2d SCFTs. In this paper we are interested in the 1D3-branes wrapped on curves in compact Calabi-Yau threefolds were studied much earlier [4], however in those setups the coupling of the D3-brane remains constant. – 1 – case where the curve C is deformable, which is in contrast to the case of the strings in 6d non-Higgsable clusters (NHC) [10], where the curve is rigid. The main novelty in our configuration is that we consider a background, where the complexified coupling τ of the N = 4 Super-Yang Mills (SYM) theory on the D3-brane varies over the internal compact dimensions. This requires a particular topological twist of the N = 4 SYM theory, which is known as the topol (...truncated)


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Christopher Couzens, Craig Lawrie, Dario Martelli, Sakura Schäfer-Nameki, Jin-Mann Wong. F-theory and AdS3/CFT2, Journal of High Energy Physics, 2017, pp. 43, Volume 2017, Issue 8, DOI: 10.1007/JHEP08(2017)043