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Register a new userIntersecting Surface Defects and Instanton Partition Functions
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We analyze intersecting surface defects inserted in interacting four-dimensional N = 2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared fixed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like configurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. Our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.
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We initiate the study of intersecting surface operators/defects in four-dimensional quantum field theories (QFTs). We characterize these defects by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom localized at a point and on intersecting surfaces in spacetime to each other and to the four-dimensional QFT. We construct supersymmetric intersecting surface defects preserving just two supercharges in N = 2 gauge theories. These defects are amenable to exact analysis by localization of the partition function of the underlying 4d/2d/0d QFT. We identify the 4d/2d/0d QFTs that describe intersecting surface operators in N = 2 gauge theories realized by intersecting M2-branes ending on N M5-branes wrapping a Riemann surface. We conjecture and provide evidence for an explicit equivalence between the squashed four-sphere partition function of these intersecting defects and correlation functions in Liouville/Toda CFT with the insertion of arbitrary degenerate vertex operators, which are labeled by representations of SU(N).
We compute the 3d N = 2 superconformal indices for 3d/1d coupled systems, which arise as the worldvolume theories of intersecting surface defects engineered by Higgsing 5d N = 1 gauge theories. We generalize some known 3d dualities, including non-Abelian 3d mirror symmetry and 3d/3d correspondence, to some of the simple 3d/1d coupled systems. Finally we propose a q-Virasoro construction for the superconformal indices.
We propose a set of novel expansions of Nekrasovs instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on $mathbb{C}^2_{q,t^{-1}} times mathbb{S}^1$, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces $mathbb{C}_{q} times mathbb{S}^1$, $mathbb{C}_{t^{-1}} times mathbb{S}^1$ and their intersection along $mathbb{S}^1$. These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with $W_{q,t}$ correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.
String instanton effects in Higgs physics are discussed through a type IIA model based on T^{6}/(Z^{2}times Z^{2}) orentifold compactifaction. By inclusion of rigid E2-branes, the model exhibits a MSSM-like spectrum, as well as extra mu and quartic Higgs couplings. These extra couplings are induced via E2 instantons non-perturbatively. Setting the string scale at 10^{18} GeV, one gets interesting TeV Higgs physics. In particlular, the tree-level Higgs mass can be uplifted substantially.
Localization methods have produced explicit expressions for the sphere partition functions of (2,2) superconformal field theories. The mirror symmetry conjecture predicts an IR duality between pairs of Abelian gauged linear sigma models, a class of which describe families of Calabi-Yau manifolds realizable as complete intersections in toric varieties. We investigate this prediction for the sphere partition functions and find agreement between that of a model and its mirror up to the scheme-dependent ambiguities inherent in the definitions of these quantities.
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