相关论文: From Quantum Monodromy to Duality
In this paper we construct a model for group field cosmology. The classical equations of motion for the non-interactive part of this model generate the Hamiltonian constraint of loop quantum gravity for a homogeneous isotropic universe…
We present $\mathcal{N}=2$ superconformal $\mathsf{U}(1)$ duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar…
We study moduli stabilization in 4D effective field theories with Sp(4,$\mathbb{Z}$) self-duality inspired by heterotic orbifold compactifications with Wilson lines. The target-space duality group of these theories is enhanced from…
Classical W-gravities and the corresponding quantum theories are reviewed. W-gravities are higher-spin gauge theories in two dimensions whose gauge algebras are W-algebras. The geometrical structure of classical W-gravity is investigated,…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N = 1 supergravity, for both the old minimal and the new minimal versions of N = 1 supergravity. We derive the self-duality equation,…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
We study the quantum moduli spaces and dynamical superpotentials of four dimensional $SU(2)^r$ linear and ring moose theories with $\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation. Nontrivial…
We establish $({\mathfrak{gl}}_M, {\mathfrak{gl}}_N)$-dualities between quantum Gaudin models with irregular singularities. Specifically, for any $M, N \in {\mathbb Z}_{\geq 1}$ we consider two Gaudin models: the one associated with the Lie…
In this paper we study arbitrary $W$ algebras related to embeddings of $sl_2$ in a Lie algebra $g$. We give a simple formula for all $W$ transformations, which will enable us to construct the covariant action for general $W$ gravity. It…
A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields.…
The role of the modular group in the holonomy representation of (2+1)-dimensional quantum gravity is studied. This representation can be viewed as a "Heisenberg picture", and for simple topologies, the transformation to the ADM…
We begin an investigation of supersymmetric theories based on exceptional groups. The flat directions are most easily parameterized using their correspondence with gauge invariant polynomials. Symmetries and holomorphy tightly constrain the…
We present families of algebraic curves describing the moduli-space of $N\!=\!2$ supersymmetric Yang-Mills theory with gauge group $SO(2n)$. We test our curves by computing the weak coupling monodromies and the number of $N\!=\!1$ vacua.
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…
Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in…
We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…