Person:

Vafa, Cumrun

We introduce T-branes, or "triangular branes," which are novel non-abelian bound states of branes characterized by the condition that on some loci, their matrix of normal deformations, or Higgs field, is upper triangular. These configurations refine the notion of monodromic branes which have recently played a key role in F-theory phenomenology. We show how localized matter living on complex codimension one subspaces emerge, and explain how to compute their Yukawa couplings, which are localized in complex codimension two. Not only do T-branes clarify what is meant by brane monodromy, they also open up a vast array of new possibilities both for phenomenological constructions and for purely theoretical applications. We show that for a general T-brane, the eigenvalues of the Higgs field can fail to capture the spectrum of localized modes. In particular, this provides a method for evading some constraints on F-theory GUTs which have assumed that the spectral equation for the Higgs field completely determines a local model.

A U(2,2|4)-invariant A-model constructed from fermionic superfields has recently been proposed as a sigma model for the superstring on (AdS_5 \times S^5). After explaining the relation of this A-model with the pure spinor formalism, the A-model action is expressed as a gauged linear sigma model. In the zero radius limit, the Coulomb branch of this sigma model is interpreted as D-brane holes which are related to gauge-invariant (\mathcal{N}=4) d=4 super-Yang-Mills operators. As in the worldsheet derivation of open-closed duality for Chern-Simons theory, this construction may lead to a worldsheet derivation of the Maldacena conjecture. Intriguing connections to the twistorial formulation of (\mathcal{N}=4) Yang-Mills are also noted.

We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant (B)-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic (D)-modules that replace the classical holomorphic curve in the quantum case.

We study (\mathcal{N})=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include higher-dimensional operators that introduce a field-dependence for the gauge coupling. We show how Feynman diagram/matrix model/string theoretic techniques can all be used to compute the IR glueball superpotential. Moreover, in the limit of turning off the superpotential, this leads to a deformation of (\mathcal{N})=2 Seiberg-Witten theory. In the case where the superpotential drives the squared gauge coupling to a negative value, we find that supersymmetry is spontaneously broken, which can be viewed as a novel mechanism for breaking supersymmetry. We propose a new duality between a class of (\mathcal{N})=1 supersymmetric U(N) gauge theories with field-dependent gauge couplings and a class of U(N) gauge theories where supersymmetry is softly broken by nonzero expectation values for auxiliary components of spurion superfields.

We study non-supersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on Calabi-Yau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the non-supersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for non-supersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.

The MSSM can arise as an orientifold of a pyramid-like quiver in the context of intersecting D-branes. Here we consider quiver realizations of the MSSM which can emerge at the bottom of a duality cascade. We classify all possible minimal ways this can be done by allowing only one extra node. It turns out that this requires extending the geometry of the pyramid to an octahedron. The MSSM at the bottom of the cascade arises in one of two possible ways, with the extra node disappearing either via Higgsing or confinement. Remarkably, the quiver of the Higgsing scenario turns out to be nothing but the quiver version of the left-right symmetric extension of the MSSM. In the minimal confining scenario the duality cascade can proceed if and only if there is exactly one up/down Higgs pair. Moreover, the symmetries of the octahedron naturally admit an automorphism of the quiver which solves a version of the (\mu) problem precisely when there are an odd number of generations.

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 conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.

We study minimal implementations of Majorana and Dirac neutrino scenarios in F-theory GUT models. In both cases the mass scale of the neutrinos (m_{\nu} \sim M_{weak}^2/\land_{UV}) arises from integrating out Kaluza-Klein modes, where (\land_{UV}) is close to the GUT scale. The participation of non-holomorphic Kaluza-Klein mode wave functions dilutes the mass hierarchy in comparison to the quark and charged lepton sectors, in agreement with experimentally measured mass splittings. The neutrinos are predicted to exhibit a "normal" mass hierarchy, with masses (m_3,m_2,m_1 \sim .05 \times (1,\alpha_{GUT}^{1/2},\alpha_{GUT})) eV. When the interactions of the neutrino and charged lepton sectors geometrically unify, the neutrino mixing matrix exhibits a mild hierarchical structure such that the mixing angles (\theta_{23}) and (\theta_{12}) are large and comparable, while (\theta_{13}) is expected to be smaller and close to the Cabibbo angle: (\theta_{13} \sim \theta_{C} \sim \alpha_{GUT}^{1/2} \sim 0.2). This suggests that (\theta_{13}) should be near the current experimental upper bound.

We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi-Yau 3-fold X. When X has no compact 4-cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the Kahler moduli space.

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value (\mu \sim 10^2 - 10^3) GeV when the hidden sector scale of supersymmetry breaking is (\sqrt{F} \sim 10^{8.5}) GeV. Further, the B(\mu) problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant (f_a \sim M_{GUT \times \mu/\wedge}), where (\wedge \sim 10^5) GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio (\mu / \wedge \sim M_{GUT}/M_{pl} \sim 10^{-3}). We find (f_a \sim 10^{12}) GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about (10^1 - 10^2) MeV, and a bino-like neutralino is (typically) the NLSP with mass of about (10^2 - 10^3) GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(\beta \sim 30 \pm 7).