We discuss the properties of lorentzian and euclidean black hole solutions of a generalized 2-dim dilaton-gravity action containing a modulus field, which arises from the compactification of heterotic string models. The duality symmetries of these solutions are also investigated.

We consider the partial difference equations of the Adler-Bobenko-Suris classification, which are characterized as multidimensionally consistent. The latter property leads naturally to the construction of auto-Bäcklund transformations and Lax pairs for all the equations in this class. Their symmetry analysis is presented and infinite hierarchies of generalized symmetries are explicitly construc...

A novel kind of generalized global symmetries is uncovered in a large class familiar 3+1-dimensional gauge theories, including the free Maxwell theory and Yang-Mills theories. These new symmetries, known as non-invertible do not have inverses thus go beyond traditional paradigm (anti-)unitary transformations. They are implemented by topological duality defects, generalizing Kramers-Wannier defe...

The local theory of symmetries of differential equations has been well-established since the days of Sophus Lie. Generalized, or higher order symmetries can be traced back to the original paper of Noether, [32], but were not exploited until the discovery that they play a critical role in integrable (soliton) partial differential equations, cf. [30, 33, 35]. While the local theory is very well d...

Lavelle-McMullan symmetry of QED is examined at classical and quantum levels. It is shown that Lavelle-McMullan symmetry does not give any new non-trivial information in QED by examining the Ward-Takahashi identities. Being inspired by the examination of Ward-Takahashi identity, we construct the generalized non-local and non-covariant symmetries of QED.

We construct second order reductions of the generalized Witten-DijkgraafVerlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction. MSC Subj. Class. 2000: 35C05, 81T60

We study the consequences of rotational symmetry breaking in isotropic vector spin glasses. Starting from a microscopic model we identify the underlying symmetries of time-dependent (replica-dependent) SO(rn) rotations. The hydrodynamic triad theory is confirmed and the spinwave stiffness is related to a generalized transverse susceptibility. An expansion around mean-field theory is used to cal...

abstract We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.

In M-theory vacua with vanishing 4-form F(4), one can invoke the ordinary Riemannian holonomy H ⊂ SO(1, 10) to account for unbroken supersymmetries n = 1, 2, 3, 4, 6, 8, 16, 32. However, the generalized holonomy conjecture, valid for non-zero F(4), can account for more exotic fractions of supersymmetry, in particular 16 < n < 32. The conjectured holonomies are given by H ⊂ G where G are the gen...

We study the solution of linear systems that typically arise in discretizations of boundary value problems on a domain with geometrical symmetries. If the discretization is done in an appropriate way, then such a system commutes with a group of permutation matrices. Recently, algorithms have been developed that exploit this special structure, however these methods are limited to the case that t...