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We describe the counting of BPS states of Type II strings on K3 by relating the supersymmetric cycles of genus $g$ to the number of rational curves with $g$ double points on K3. The generating function for the number of such curves is the…
In an earlier work it was shown that the IR singularities arising in the nonplanar one loop two point function of a noncommutative ${\cal N}=2$ gauge theory can be reproduced exactly from the massless closed string exchanges. The…
Exploiting the gauge/gravity correspondence we find the spectrum of hadronic-like bound states of adjoint particles with a large global charge in several confining theories. In particular, we consider an embedding of four-dimensional N=1…
We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a…
Large N duality conjecture between U(N) Chern-Simons gauge theory on $S^3$ and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the…
We present a general analysis of all the possible soft breakings of N=2 supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all the couplings…
We develop the harmonic space method for conifold and use it to study local complex deformations of $T^{\ast}S^{3}$ preserving manifestly $SL(2,C) $ isometry. We derive the perturbative manifestly $SL(2,C) $ invariant partition function…
We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for…
In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which…
We show that the duality phase transition in the unoriented type I theory of open and closed strings is_first order_. The order parameter is the semiclassical approximation to the heavy quark-antiquark potential at finite temperature,…
We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix…
A formula was recently proposed for the perturbative partition function of certain $\mathcal N=1$ gauge theories on the round four-sphere, using an analytic-continuation argument in the number of dimensions. These partition functions are…
We extend the methods of Spradlin and Volovich to compute the partition function for a conformally-invariant gauge theory on R x S^3 in which the dilatation operator is represented by a spin-chain Hamiltonian acting on pairs of states, not…
The topological string partition function Z=exp(lambda^{2g-2} F_g) is calculated on a compact Calabi-Yau M. The F_g fulfill the holomorphic anomaly equations, which imply that Z transforms as a wave function on the symplectic space…
We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. The predicted equations are derived in this model, and new equations can be discovered as well.…
We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d $\mathcal{N}=1$ gauge theory partition function on the Omega-deformed background $\mathbb{R}^4_{\epsilon_{1,2}}\times…
We develop a new class of clockwork theories with an augmented structure of the near-neighbour interactions along a one-dimensional closed chain. Such a topology leads to new and attractive features in addition to generating light states…
We establish the universal edge scaling limit of random partitions with the infinite-parameter distribution called the Schur measure. We explore the asymptotic behavior of the wave function, which is a building block of the corresponding…
We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through $Z_{12-I}$ orbifold compactification. It is…
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The…