Vortex loop operators, M2-branes and holography

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N=2 S-duality via Outer-automorphism Twists

Compactification of 6d N=(2,0) theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4d N=2 theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume fields are transformed by the discrete symmetries associated to those of the Dynkin diagram of type G. This allows us to generate more S-dualities, and in particular to reproduce a couple of S-dual pairs found previously by Argyres and Wittig.Comment: 8 pages, 6 figure

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.Comment: 41 page

Supersymmetric D-branes in the D1-D5 background

We construct supersymmetric D-brane probe solutions in the background of the 2-charge D1-D5 system on M, where M is either K3 or T^4. We focus on `near-horizon bound states' that preserve supersymmetries of the near-horizon AdS_3 x S^3 x M geometry and are static with respect to the global time coordinate. We find a variety of half-BPS solutions that span an AdS_2 subspace in AdS_3, carry worldvolume flux and can wrap an S^2 within S^3 and/or supersymmetric cycles in M.Comment: Latex, 24 pages. v2: references added, modified Discussion, published versio

Superconformal Index with Duality Domain Wall

We study a superconformal index for ${\cal N}=4$ super Yang-Mills on $S^1 \times S^3$ with a half BPS duality domain wall inserted at the great two-sphere in $S^3$. The index is obtained by coupling the 3d generalized superconformal index on the duality domain wall with 4d half-indices. We further consider insertions of line operators to the configuration and propose integral equations which express that the 3d index on duality domain wall is a duality kernel relating half indices of two line operators related by the duality map. We explicitly check the proposed integral equations for various duality domain walls and line operators in the ${\cal N}=4$ SU(2) theory. We also briefly comment on a generalization to $\mathcal{N}=2$ $A_1$ Gaiotto theories with a simple example, ${\cal N}=2$ SU(2) SYM with four flavors.Comment: v1: 25 pages, 4 figures. v2: comments and a reference added, minor corrections. v3: 30 pages, new results and discussions added to sec 4.5 and sec 5.1, eq 49 and eq 51 corrected, text improved; to appear in JHE

The Virtue of Defects in 4D Gauge Theories and 2D CFTs

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories - which we construct - and loop operators and domain wall operators in four dimensional N=2 supersymmetric gauge theories on S^4. Our computation of the correlation functions in Liouville/Toda theory in the presence of topological defect operators, which are supported on curves on the Riemann surface, yields the exact answer for the partition function of four dimensional gauge theories in the presence of various walls and loop operators; results which we can quantitatively substantiate with an independent gauge theory analysis. As an interesting outcome of this work for two dimensional conformal field theories, we prove that topological defect operators and the Verlinde loop operators are different descriptions of the same operators.Comment: 59 pages, latex; v2 corrections to some formula

Surface Operators in Abelian Gauge Theory

We consider arbitrary embeddings of surface operators in a pure, non-supersymmetric abelian gauge theory on spin (non-spin) four-manifolds. For any surface operator with a priori simultaneously non-vanishing parameters, we explicitly show that the parameters transform naturally under an SL(2, Z) (or a congruence subgroup thereof) duality of the theory. However, for non-trivially-embedded surface operators, exact S-duality holds only if the quantum parameter effectively vanishes, while the overall SL(2, Z) (or a congruence subgroup thereof) duality holds up to a c-number at most, regardless. Via the formalism of duality walls, we furnish an alternative derivation of the transformation of parameters - found also to be consistent with a switch from Wilson to 't Hooft loop operators under S-duality. With any background embedding of surface operators, the partition function and the correlation functions of non-singular, gauge-invariant local operators on any curved four-manifold, are found to transform like modular forms under the respective duality groups.Comment: 30 pages. Minor refinemen

Scattering in Mass-Deformed N>=4 Chern-Simons Models

We investigate the scattering matrix in mass-deformed N>=4 Chern-Simons models including as special cases the BLG and ABJM theories of multiple M2 branes. Curiously the structure of this scattering matrix in three spacetime dimensions is equivalent to (a) the two-dimensional worldsheet matrix found in the context of AdS/CFT integrability and (b) the R-matrix of the one-dimensional Hubbard model. The underlying reason is that all three models are based on an extension of the psu(2|2) superalgebra which constrains the matrix completely. We also compute scattering amplitudes in one-loop field theory and find perfect agreement with scattering unitarity.Comment: 63 pages, v2: minor corrections, v3: minor improvement

Charged particle-like branes in ABJM

We study the effect of adding lower dimensional brane charges to the 't Hooft monopole, di-baryon and baryon vertex configurations in $AdS_4 \times \mathbb{P}^3$. We show that these configurations capture the background fluxes in a way that depends on the induced charges, and therefore, require additional fundamental strings in order to cancel the worldvolume tadpoles. The study of the dynamics reveals that the charges must lie inside some interval in order to find well defined configurations, a situation familiar from the baryon vertex in $AdS_5 \times S^5$ with charges. For the baryon vertex and the di-baryon the number of fundamental strings must also lie inside an allowed interval. Our configurations are sensitive to the flat $B$-field recently suggested in the literature. We make some comments on its possible role. We also discuss how these configurations are modified in the presence of a non-zero Romans mass.Comment: 31 pages, 14 figures, discussion of charges improved, published versio