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In recent work Alexandre, Ellis, Millington and Seynaeve have extended the Goldstone theorem to non-Hermitian Hamiltonians that possess a discrete antilinear symmetry such as $PT$. They restricted their discussion to those realizations of…
We consider systems in which a continuous symmetry $G$, which may be anomalous, is spontaneously broken to an anomaly-free subgroup $H$ such that the effective action for the Goldstone modes contains topologically non-trivial terms. If the…
Motivated by the possibility that physics may be effectively five-dimensional over some range of distance scales, we study the possible gaugings of five-dimensional N=2 supergravity. Using a constructive approach, we derive the conditions…
In this article I first give an abbreviated history of string theory and then describe the recently-conjectured field-string duality. This suggests a class of nonsupersymmetric gauge theories which are conformal (CGT) to leading order of…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
We consider the analogue of Seiberg duality for two-dimensional $N=(2,2)$ gauge theory with orthogonal gauge groups and with fundamental chiral multiplets proposed by Hori. Following Hori, when we consider $O(N)$ gauge group as the…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
We construct off-shell superconformal actions of hypermultiplets coupled with non-Abelian gauge multiplets in three-dimensional N = 3 and N = 4 projective superspaces. We establish the explicit embeddings of the N = 2 vector and adjoint…
One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the…
We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…
We discuss the coupling of vector-tensor multiplets to N=2 supergravity.
We show that scattering amplitudes in magical, symmetric or homogeneous N=2 Maxwell-Einstein supergravities can be obtained as double copies of two gauge theories, using the framework of color/kinematics duality. The left-hand-copy is N=2…
A solution of the doublet-triplet splitting problem in the supersymmetric $SU(6)$ gauge theory is suggested. The `missing doublet' multiplet -- 175-plet of the $SU(6)$ group as well as the custodial $SU(2)_{cus}$ global symmetry play…
We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that…
We consider the standard gauge theory of Poincar\'{e} group, realizing as a subgroup of $GL(5. R)$. The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this…
In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far…
Using the formulation for N=2 conformal supergravity in SU(2) superspace, we define super-Weyl (or superconformal) anomalies and construct two types of nonlocal effective actions that generate these anomalies. We also present the local…
We propose a new gauge prepotential $\Upsilon_i$ describing the four-dimensional ${\mathcal N}=2$ superconformal gravitino multiplet. The former naturally arises via a superspace reduction of the ${\mathcal N}=3$ conformal supergravity…
We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of…
We derive the general supertrace formula for a system with $N$ chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral…