The Coulomb Branch of 3d N = 4 Theories Mathew Bullimore Tudor Dimofte Davide Gaiotto PS rhiomo lto r NIn sttuitru tl S oir Tn h so rI ntis ti tluPt h yosri As Wv nt rl ooS tuO Ny NPr iLn Yto n CN
We discuss the integrability and wall-crossing properties of Kondo problems, where an 1d impurity is coupled to a 2d chiral CFT and triggers a defect RG flow. We review several new and old examples inspired by constructions in four-dimensional Chern-Simons theory and by affine Gaudin models.
We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the “Orbifold groupoids” which control the composition of orbifold operations. Three-dimensional TQFT’s of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications...
AbstractWe compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional \( \mathcal{N} \) = 4 Super Yang-Mills theory. We use the indices as very stringent tests of a variety of string theory-inspired conjectures about the action of S-duality on such defects.
Abstract We discuss the classification of SPT phases in condensed matter systems. We review Kitaev’s argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum of gapped physical systems [20, 23]. We propose a concrete description of that spectrum and of the corresponding cohomology theory. We compare our proposal to pre-existing...
Abstract We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d \( \mathcal{N} \) = 4 gauge theories. We conjecture various relations between these boundary VOA’s and properties of the (topologically twisted) bulk theories. We discuss applications to the Symplectic Duality and Geometric Langlands programs.
Abstract A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling τ in the upper-half plane and by the choice of the CFT in the decoupling limit τ → ∞. Upon performing an SL(2, ℤ) transformation in the...
Abstract We formulate a conjectural relation between the category of line defects in topologically twisted 3d \( \mathcal{N} \) = 4 supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for the theories. We test the conjecture in several examples and provide some partial proofs for standard classes of gauge theories.
Gaiotto Open Access Regular Article - Theoretical Physics First Online: 12 February 2019 Abstract Three-dimensional \( \mathcal{N} \) = 4 supersymmetric quantum field theories admit two topological
Abstract We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in \( \mathcal{N} \) = 4 Super Yang Mills gauge theory. These vertex algebras satisfy non-trivial duality relations inherited from S-duality of the four-dimensional gauge theory. The gauge theory construction equips the vertex algebras with collections of modules...
Abstract We study the dynamics of certain 3d \( \mathcal{N}=1 \) time reversal invariant theories. Such theories often have exact moduli spaces of supersymmetric vacua. We propose several dualities and we test these proposals by comparing the deformations and supersymmetric ground states. First, we consider a theory where time reversal symmetry is only emergent in the infrared...
Abstract We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d \( \mathcal{N}=2 \) gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation of supersymmetric indices. Examples include basic abelian dualities, level-rank dualities, and Aharony dualities.
Abstract We conjecture a formula for the Schur index of four-dimensional \( \mathcal{N}=2 \) theories coupled to (2, 2) surface defects in terms of the 2d-4d BPS spectrum in the Coulomb phase of the theory. The key ingredient in our conjecture is a refined 2d-4d wall-crossing invariant, which we also formulate. Our result intertwines recent conjectures expressing the four...
We investigate superconformal surface defects in four-dimensional \( \mathcal{N}=2 \) superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions...
SU(N ) gauge theory is time reversal invariant at θ = 0 and θ = π. We show that at θ = π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at θ = π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ = 0 is gapped, non-degenerate...
It is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic “shadow” theories, which are obtained from the original theory by “gauging fermionic parity”. The fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a one-form symmetry generated by quasi-particles with...
We propose an explicit description of “duality walls” which encode at low energy the global symmetry enhancement expected in the UV completion of certain five-dimensional gauge theories. The proposal is supported by explicit localization computations and implies that the instanton partition function of these theories satisfies novel and unexpected integral equations.
Abstract We conjecture a formula for the Schur index of four-dimensional \( \mathcal{N}=2 \) theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or...
Abstract We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is valid for defects which can be given a “vortex construction”, i.e. can be defined by RG flow from vortex configurations in a larger...
