Related papers: Symplectic Structure in Brane Mechanics

We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a…

We consider probe p-branes dynamics in string theory backgrounds of general type. We use an action, which interpolates between Nambu-Goto and Polyakov type actions. This allows us to give a unified description for the tensile and…

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…

In this work we study the dynamics of branes on group manifolds G deep in the stringy regime. After giving a brief overview of the various branes that can be constructed within the boundary conformal field theory approach, we analyze in…

Using exact boundary conformal field theory methods we analyze the D-brane physics of a specific four-dimensional non-critical superstring theory which involves the N=2 SL(2)/U(1) Kazama-Suzuki model at level 1. Via the holographic duality…

Variational integrators have traditionally been constructed from the perspective of Lagrangian mechanics, but there have been recent efforts to adopt discrete variational approaches to the symplectic discretization of Hamiltonian mechanics…

We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This…

We study certain aspects of noncommutativity in field theory, strings and membranes. We analyse the dynamics of an open membrane whose boundary is attached to p-branes. Noncommutative features of the boundary string coordinates are revealed…

We study D=3 field theories on the D3-branes stretched between two NS5-branes with NS B-field background. The theory is a noncommutative gauge theory. The mirror symmetry and S-duality of the theory are discussed. A new feature is that the…

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…

In this work we employ a field theoretical approach to explain the nature of the non-conserved spin current in spintronics. In particular, we consider the usual U(1) gauge theory for the electromagnetism at classical level in order to…

We use the M theory approach of Witten to investigate N=1 SU($N_c$) SQCD with $N_f$ flavors. We reproduce the field theoretical results and identify in M theory the gluino condensate and the eigenvalues of the meson matrix. This approach…

The properties of the D-brane fluctuations are investigated using the two types of deformation of the Dirac structure, based on the B-transformation and the beta-transformation, respectively. The former gives the standard gauge theory with…

The (pre)multisymplectic geometry of the De Donder--Weyl formalism for field theories is further developed for a variety of field theories including a scalar field theory from the canonical Klein-Gordon action, the electric and magnetic…

We give a generally covariant description, in the sense of symplectic geometry, of gauge transformations in Batalin-Vilkovisky quantization. Gauge transformations exist not only at the classical level, but also at the quantum level, where…

Following Dirac's brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by…

We discuss the interplay between lagrangian distributions and connections in symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic…

This article generalizes the theory of shifted symplectic structures to the relative context and non-geometric stacks. We describe basic constructions that naturally appear in this theory: shifted cotangent bundles and the AKSZ procedure.…

We present a comprehensive formalism to derive precise expressions for the induced gravity of the braneworld, assuming the dynamics of the Dirac-Nambu-Goto type. The quantum fluctuations of the brane at short distances give rise to…

This expository article elaborates upon my talk at the 2025 AMS Summer Institute on Algebraic Geometry. It gives an introduction to a conjecture from Tate's 1966 S\'eminaire Bourbaki report, predicting the existence of a symplectic form on…