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)