We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 and show that it admits dual descriptions: either as an integral over Coulomb branch or a sum vortex anti-vortex excitations Higgs branches theory. further demonstrate correlation functions in Liouville/Toda CFT for class theories, thereby uncovering novel modular properties theories. Some these flow infrared to Calabi-Yau sigma models - such conifold topology changing flop transition is realized...

A bstract We study ℤ N one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, associated TFT five-dimensional bulk is BF model. revisit its canonical quantization and construct boundary states on several important classes of four manifolds that are spin, non-spin torsional. highlight a web dualities, which can be naturally interpreted within SymTFT framework. also point out an intriguing class exhibit mixed ’t...

We find a 16-supersymmetric mass-deformed Bagger-Lambert theory with $SO(4)\ifmmode\times\else\texttimes\fi{}SO(4)$ global $R$ symmetry. The charge plays the role of noncentral term in superalgebra. This has one symmetric vacuum and two inequivalent broken sectors vacua. Each sector symmetry $SO(4)$ geometry. $1/2$ BPS domain walls connecting phase any phase, $1/4$ supertubelike objects, which may appear as anyonic $q$-balls or vortices phase. also discuss mass deformations, reduce number...

We compute the equivariant elliptic genera of several classes ALE and ALF manifolds using localization in gauged linear sigma models. In model computation action corresponds to chemical potentials for U(1) currents exhibit interesting pole structure as a function potentials. use this decompose answers into polar terms that wall crossing universal terms. compare our results previous on large radius limit Taub-NUT genus also discuss applications counting BPS world-sheet spectrum monopole...

Abstract We define modular linear differential equations (MLDE) for the level-two congruence subgroups $\Gamma_\theta$, $\Gamma^0(2)$ and $\Gamma_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one spin structures on torus. The pole fermionic MLDEs are investigated by exploiting valence formula subgroups. focus first- second-order holomorphic without poles use them find a large class “fermionic rational conformal field theories” (fermionic RCFTs), which have non-negative...

We study constraints coming from the modular invariance of partition function two-dimensional conformal field theories. constrain spectrum CFTs in presence holomorphic and anti-holomorphic currents using semi-definite programming. In particular, we find bounds on twist gap for non-current primaries depend dramatically currents, showing numerous kinks peaks. Various rational are realized at numerical boundary gap, saturating upper limits degeneracies. Such theories include Wess-Zumino-Witten...

A bstract We constrain the spectrum of $$ \mathcal{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (1, 1) and (2, 2) superconformal field theories in two-dimensions by requiring NS-NS sector partition function to be invariant under Γ θ congruence subgroup full modular group SL(2, ℤ). employ semi-definite programming find constraints on allowed operators with or without U(1) charges. Especially, upper bounds twist gap for noncurrent primaries...

A bstract Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γ θ , 0 (2) and of SL 2 (ℤ) was developed used to classify fermionic rational conformal field theories (RCFT). Two character solutions second-order MLDE without poles were found their corresponding CFTs are identified. Here we extend this analysis explore landscape three RCFTs obtained from third-order poles. Especially, focus on a class whose Neveu-Schwarz sector vacuum has no free-fermion...

A bstract Given a two-dimensional bosonic theory with non-anomalous ℤ 2 symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF level 2. From Hamiltonian perspective, information of dualities is encoded in topological boundary state which defined as an eigenstate certain Wilson loop operators (anyons) bulk. We generalize this story to theories N focusing on parafermionization. find generic defining different states including...

We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi data. Via bulk-boundary correspondence, they related three-dimensional Haagerup topological theories, recently constructed by twisting N=4 rank-zero superconformal (SCFTs), called S-fold SCFTs. propose that, up overall factors, half-indices SCFTs give explicit Nahm representation four characters RCFTs including vacuum...

In gauge theories on a spacetime equipped with circle, the holonomy variables, living in Cartan torus, play special roles. With their periodic nature properly taken into account, we find that supersymmetric theory $d$ dimensions tends to reduce small radius limit disjoint sum of multiple $(d-1)$ dimensional at distinct holonomies, called $H$-saddles. The phenomenon occurs regardless dimensions, and here explore such $H$-saddles for $d=4$ $\cal N=1$ $T^2$ fibred over $\Sigma_g$, limits...