200 citations · 1.6k across the 65 of their papers we have counts for
18 papers · 1 filter
Berezin quantization, conformal welding and the Bott-Virasoro group
A. Alekseev, S. Shatashvili, L. Takhtajan
Following Nag-Sullivan, we study the representation of the group of diffeomorphisms of the circle on the Hilbert space of holomorphic functions. Conformal weldi…
Characters, Coadjoint Orbits and Duistermaat-Heckman Integrals
Anton Alekseev, Samson L. Shatashvili
The asymptotics of characters of irreducible representations of a compact Lie group for large values of the scaling factor are given by Duistermaat-Heck…
Provenance of classical Hamiltonian time crystals
Anton Alekseev, Dai Jin, Antti J. Niemi
Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is…
Coadjoint Orbits, Cocycles and Gravitational Wess-Zumino
Anton Alekseev, Samson L. Shatashvili
About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for char…
Wilson surface observables from equivariant cohomology
Anton Alekseev, Olga Chekeres, Pavel Mnev
Wilson lines in gauge theories admit several path integral descriptions. The first one (due to Alekseev-Faddeev-Shatashvili) uses path integrals over coadjoint orbits. The second o…
One-dimensional Chern-Simons theory
Anton Alekseev, Pavel Mnev
We study a one-dimensional toy version of the Chern-Simons theory. We construct its simplicial version which comprises features of a low-energy effective gauge theory and of a topo…
Quantization of Wilson loops in Wess-Zumino-Witten models
Anton Alekseev, Samuel Monnier
We describe a non-perturbative quantization of classical Wilson loops in the WZW model. The quantized Wilson loop is an operator acting on the Hilbert space of closed strings and c…
Current Algebras and Differential Geometry
Anton Alekseev, Thomas Strobl
We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma models are described by a new type of a current algebra. The currents are labeled by pairs of a…
Non-commutative gauge theory of twisted D-branes
Anton Yu. Alekseev, Stefan Fredenhagen, Thomas Quella +1
In this work we propose new non-commutative gauge theories that describe the dynamics of branes localized along twisted conjugacy classes on group manifolds. Our proposal is based…
Open Strings and Non-commutative Geometry of Branes on Group Manifolds
Anton Yu. Alekseev, Andreas Recknagel, Volker Schomerus
In this contribution we review some recent work on the non-commutative geometry of branes on group manifolds. In particular, we show how fuzzy spaces arise in this context from an…
RR charges of D2-branes in the WZW model
Anton Alekseev, Volker Schomerus
We consider the contribution of the B-field into the RR charge of a spherical D2-brane. Extending a recent analysis of Taylor, we show that the boundary and bulk contributions do n…
On area and entropy of a black hole
A. Alekseev, A. P. Polychronakos, M. Smedbäck
We consider a model of a black hole consisting of a number of elementary components. Examples of such models occur in the Ashtekar's approach to canonical Quantum Gravity and in M-…
Wilson lines on noncommutative tori
Anton Alekseev, Andrei Bytsko
We introduce the notion of a monodromy for gauge fields with vanishing curvature on the noncommutative torus. Similar to the ordinary gauge theory, traces of the monodromies define…
Closed constraint algebras and path integrals for loop group actions
A. Y. Alekseev, V. Schomerus, T. Strobl
In this note we study systems with a closed algebra of second class constraints. We describe a construction of the reduced theory that resembles the conventional treatment of first…
Combinatorial quantization of the Hamiltonian Chern-Simons theory I
A. Yu. Alekseev, H. Grosse, V. Schomerus
Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons th…
Symplectic structure of the moduli space of flat connections on a Riemann surface
A. Yu. Alekseev, A. Z. Malkin
We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus with marked points. For ${\g}$ being a semisimple Li…
Integrability in Hamiltonian Chern-Simons theory
A. Yu. Alekseev
We consider the moduli space of flat connections on the Riemann surface with marked points. The new efficient parametrization is suggested and used to construct an integrable model…
Symplectic structures associated to Lie-Poisson groups
A. Yu. Alekseev, A. Z. Malkin
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are…