We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence of three point functions in the squeezed limit for general settings of quasi-single field inflation. Our framework can be also applied to inflation models with heavy particles. We make a qualitative discussion on the effects of heavy particles during inflation and those of sudden turning trajectory in our framework.

We initiate a systematic study of 2d (0, 2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theory. Finally, we introduce Brane Brick Models, a novel class of brane configurations that consist of D4-branes suspended from an NS5-brane wrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are the 2d analogues of Brane Tilings and allow a direct connection between geometry and gauge theory.

We argue a squashing deformation of 3D N = 2 supersymmetric theories on round S 3 , which preserves SU (2) L × U (1)r isometry and the supersymmetries. We stress that the choice of a supersymmetry for the localization affects whether the partition function calculated using the supersymmetry depends on the squashing parameter or not.

We investigate a squashing deformation of 3d N = 2 supersymmetric theories on three-sphere, which have four supercharges. The deformation preserves SU(2) L ×U(1) r isometry and all four supersymmetries. We compute the partition function and find non-trivial dependence on the squashing parameter. We also consider the large N limit of a certain class of quiver gauge theories which have free energy of order N 3/2 , and show that the free energy on the squashed sphere differs from that on round sphere by a certain factor depending only on the squashing parameter. *