Related papers: Integrable Field Theories derived from 4D Self-dua…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to…
The dual relationship between two n-1 parameter families of quantum field theories based on extended complex numbers is investigated in two dimensions. The non-local conserved charges approach is used. The lowest rank affine Toda field…
It is well known that by using the infinite dimensional symmetries that issue from string theories, one can build 2D geometric field theories. These 2D field theories can be identified with gravitational and gauge anomalies that arise in…
Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the…
We suggest a conformally invariant generalization of string theory to higher-dimensional objects. As such a model, we consider a conformally invariant $\sigma$ model. For this theory, the Hamiltonian formalism is constructed, and the full…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single…
We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We…
In a previous paper with Gibbons [CMP 120 (1987) 295] we derived a list of three dimensional symmetric space $\sigma$-model obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and…
It is shown that target space diffeomorphism invariance of a generic Lagrangian for a set of scalar fields leads to an analog of Einstein equations for the geometry of a level set of these fields.
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to…
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an $\mathrm{O}(D,D)$ covariant…
Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…
A family of wave solutions to the full Einstein equations in AdS_5 geometry is derived. These background solutions give by duality the response of N=4 SYM at strong coupling to an arbitrary distribution of fast moving external sources for…
Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection on a superbundle. We propose to take as superbundle the exterior algebra obtained from a Hermitian bundle with structure group U(n).…
We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but…
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any…
This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual)…
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating…