Advanced search    

Search: authors:"Cumrun Vafa"

21 papers found.
Use AND, OR, NOT, +word, -word, "long phrase", (parentheses) to fine-tune your search.

D-type conformal matter and SU/USp quivers

Abstract We discuss the four dimensional models obtained by compactifying a single M5 brane probing D N singularity (minimal D-type (1, 0) conformal matter in six dimensions) on a torus with flux for abelian subgroups of the SO(4N) flavor symmetry. We derive the resulting quiver field theories in four dimensions by first compactifying on a circle and relating the flux to duality...

Superconformal index, BPS monodromy and chiral algebras

We show that specializations of the 4d \( \mathcal{N}=2 \) superconformal index labeled by an integer N is given by Tr ℳ N where ℳ is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras \( {\mathcal{A}}_N \). This generalizes the recent...

Fivebranes and 3-manifold homology

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically...

Elliptic genus of E-strings

We study a family of 2d \( \mathcal{N}=\left(0,\ 4\right) \) gauge theories which describes at low energy the dynamics of E-strings, the M2-branes suspended between a pair of M5 and M9 branes. The gauge theory is engineered using a duality with type IIA theory, leading to the D2-branes suspended between an NS5-brane and 8 D8-branes on an O8-plane. We compute the elliptic genus of...

4d \( \mathcal{N}=1 \) from 6d (1, 0)

We study the geometry of 4d \( \mathcal{N}=1 \) SCFT’s arising from compactification of 6d (1, 0) SCFT’s on a Riemann surface. We show that the conformal manifold of the resulting theory is characterized, in addition to moduli of complex structure of the Riemann surface, by the choice of a connection for a vector bundle on the surface arising from flavor symmetries in 6d. We...

Quadrality for supersymmetric matrix models

We introduce a new duality for \( \mathcal{N} \) = 1 supersymmetric gauged matrix models. This 0d duality is an order 4 symmetry, namely an equivalence between four different theories, hence we call it Quadrality. Our proposal is motivated by mirror symmetry, but is not restricted to theories with a D-brane realization and holds for general \( \mathcal{N} \) = 1 matrix models. We...

F-theory and \( \mathcal{N} \) = 1 SCFTs in four dimensions

Using the F-theory realization, we identify a subclass of 6d (1,0) SCFTs whose compactification on a Riemann surface leads to \( \mathcal{N} \) = 1 4d SCFTs where the moduli space of the Riemann surface is part of the moduli space of the theory. In particular we argue that for a special case of these theories (dual to M5 branes probing ADE singularities), we obtain 4d \( \mathcal...

Punctures for theories of class \( {\mathcal{S}}_{\varGamma } \)

With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class \( {\mathcal{S}}_{\varGamma } \). The class \( {\mathcal{S}}_{\varGamma } \) theories arise from M5-branes probing ℂ 2/Γ, an ADE singularity. The resulting 4D theories descend from compactification on Riemann surfaces decorated with...

Brane brick models in the mirror

Brane brick models are Type IIA brane configurations that encode the 2d \( \mathcal{N}=\left(0,2\right) \) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror...

Geometric engineering, mirror symmetry and \( 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} \)

We study compactification of 6 dimensional (1,0) theories on T 2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d \( \mathcal{N}=2 \) geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many...

F-Theory, spinning black holes and multi-string branches

We study 5d supersymmetric black holes which descend from strings of generic \( \mathcal{N}=\left(1,\kern0.5em 0\right) \) supergravity in 6d. These strings have an F-theory realization in 6d as D3 branes wrapping smooth genus g curves in the base of elliptic 3-folds. They enjoy (0, 4) worldsheet supersymmetry with an extra SU(2) L current algebra at level g realized on the left...

Geometry of 6D RG flows

We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: one corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as...

tt * geometry in 3 and 4 dimensions

We consider the vacuum geometry of supersymmetric theories with 4 supercharges, on a flat toroidal geometry. The 2 dimensional vacuum geometry is known to be captured by the tt * geometry. In the case of 3 dimensions, the parameter space is (T 2 × \( \mathbb{R} \)) N and the vacuum geometry turns out to be a solution to a generalization of monopole equations in 3N dimensions...

6d Conformal matter

A single M5-brane probing G, an ADE-type singularity, leads to a system which has G × G global symmetry and can be viewed as “bifundamental” (G, G) matter. For the A N series, this leads to the usual notion of bifundamental matter. For the other cases it corresponds to a strongly interacting (1, 0) superconformal system in six dimensions. Similarly, an ADE singularity...

On the classification of 6D SCFTs and generalized ADE orbifolds

We study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity ℂ2/Γ with Γ a discrete subgroup of U(2). When Γ is a subgroup of SU (2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2, 0) SCFTs. For more general U(2) subgroups, the...

Tangles, generalized Reidemeister moves, and three-dimensional mirror symmetry

Three-dimensional \( \mathcal{N} \) = 2 superconformal field theories are constructed by compactifying M5-branes on three-manifolds. In the infrared the branes recombine, and the physics is captured by a single M5-brane on a branched cover of the original ultraviolet geometry. The branch locus is a tangle, a one-dimensional knotted submanifold of the ultraviolet geometry. A...

Non-perturbative topological strings and conformal blocks

We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is...