The Seiberg-Witten Kahler Potential as a Two-Sphere Partition Function

Recently it has been shown that the two-sphere partition function of a gauged linear sigma model of a Calabi-Yau manifold yields the exact quantum Kahler potential of the Kahler moduli space of that manifold. Since four-dimensional N=2 gauge theories can be engineered by non-compact Calabi-Yau threefolds, this implies that it is possible to obtain exact gauge theory Kahler potentials from two-sphere partition functions. In this paper, we demonstrate that the Seiberg-Witten Kahler potential can indeed be obtained as a two-sphere partition function. To be precise, we extract the quantum Kahler metric of 4D N=2 SU(2) Super-Yang-Mills theory by taking the field theory limit of the Kahler parameters of the O(-2,-2) bundle over P1 x P1. We expect this method of computing the Kahler potential to generalize to other four-dimensional N=2 gauge theories that can be geometrically engineered by toric Calabi-Yau threefolds.Comment: 12 pages + appendix; v2: minor corrections, reference adde

A-twisted correlators and Hori dualities

The Hori-Tong and Hori dualities are infrared dualities between two-dimensional gauge theories with $\mathcal{N}{=}(2,2)$ supersymmetry, which are reminiscent of four-dimensional Seiberg dualities. We provide additional evidence for those dualities with $U(N_c)$, $USp(2N_c)$, $SO(N)$ and $O(N)$ gauge groups, by matching correlation functions of Coulomb branch operators on a Riemann surface $\Sigma_g$, in the presence of the topological $A$-twist. The $O(N)$ theories studied, denoted by $O_+ (N)$ and $O_- (N)$, can be understood as $\mathbb{Z}_2$ orbifolds of an $SO(N)$ theory. The correlators of these theories on $\Sigma_g$ with $g > 0$ are obtained by computing correlators with $\mathbb{Z}_2$-twisted boundary conditions and summing them up with weights determined by the orbifold projection.Comment: 45 pages plus appendix; v2: updated bibliography and acknowledgement

Quantization of anomaly coefficients in 6D N=(1,0)\mathcal{N}=(1,0) supergravity

We obtain new constraints on the anomaly coefficients of 6D $\mathcal{N}=(1,0)$ supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group $G$ should be an element of $2 H^4(BG;\mathbb{Z}) \otimes \Lambda_S$ where $\Lambda_S$ is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.Comment: 42 pages. v3: Some clarifications, typos correcte

On the Defect Group of a 6D SCFT

We use the F-theory realization of 6D superconformal field theories (SCFTs) to study the corresponding spectrum of stringlike, i.e. surface defects. On the tensor branch, all of the stringlike excitations pick up a finite tension, and there is a corresponding lattice of string charges, as well as a dual lattice of charges for the surface defects. The defect group is data intrinsic to the SCFT and measures the surface defect charges which are not screened by dynamical strings. When non-trivial, it indicates that the associated theory has a partition vector rather than a partition function. We compute the defect group for all known 6D SCFTs, and find that it is just the abelianization of the discrete subgroup of U(2) which appears in the classification of 6D SCFTs realized in F-theory. We also explain how the defect group specifies defining data in the compactification of a (1,0) SCFT.Comment: 24 page

FPU physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. We find the thermalization rate $\Gamma$ to be independent of radius and scaling as $\Gamma\sim T^*/\epsilon_{{\rm pre}}^2$, where $T^*$ and $\epsilon_{{\rm pre}}$ are effective resonator temperature and prestrain