Related papers: On the Exact Quantum Integrability of the Membrane
We examine the algebraic structure of the matrix regularization for the wrapped membrane on $R^{10}\times S^1$ in the light-cone gauge. We give a concrete representation for the algebra and obtain the matrix string theory having the…
It is shown that the mass spectrum of supermembrane theory is continuous. This fact is due to the trivial circumstance that a membrane can emit "needles" of zero area with no cost in energy. In supersymmetric case, this classical degeneracy…
We systematically construct and study smooth supersymmetric solutions in 5 dimensional N=1 Yang-Mills-Einstein supergravity. Our solution is based on the ADHM construction of (dyonic) multi-instantons in Yang-Mills theory, which extends to…
In this paper we prove that the full symmetric Toda system is integrable in the sense of the Lie-Bianchi criterion, i.e. that there exists a solvable Lie algebra of vector fields of dimension $N=\dim M$ on the phase space $M$ of this system…
We discuss an exact time dependent O(3) symmetric solution with a horizon of the 5d AdS classical gravity equations searching for a 4d boundary theory which would correspond to expanding gauge theory matter. The boundary energy-momentum…
We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive,…
We study the quantum cosmology of a flat Friedmann-Lema\^{i}tre-Robertson-Walker universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the…
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of certain complexes, which are modeled on the…
We study spiky configurations of membranes in the SO(d)xSU(N) invariant matrix models. A class of exact solutions (analogous to plane-waves) of the corresponding Schroedinger equation for an arbitrary N is discussed. If the large N limit is…
We construct various exact analytical solutions of the $SO(3)$ BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori.These are also solutions of Yang Mills theory compactified on a sphere times time and they are…
We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a compact Riemann surface, and invariance is assumed under rotations of $S^2$. It is well known that the self-duality equations in this set-up reduce to vortex…
It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra $sl(3)$. The gauge-rotated Hamiltonians, as well as their integrals of motion, once rewritten in appropriate…
In this paper the spherical case of the Whittaker Inversion Theorem is given a relatively self-contained proof. This special case can be used as a help in deciphering the handling of the continuous spectrum in the proof of the full theorem.…
We construct new solutions of ten-dimensional supergravity with sixteen supercharges which describe the backreaction of D$p$-branes with spherical worldvolume. These solutions are holographically dual to the $(p+1)$-dimensional maximally…
We study $N$=2 supersymmetric integrable theories with spontaneously-broken \Zn\ symmetry. They have exact soliton masses given by the affine $SU(n)$ Toda masses and fractional fermion numbers given by multiples of $1/n$. The basic such…
We study the maximally supersymmetric Yang-Mills theory on $S^d$ using supersymmetric localisation and holography. We argue that the analytic continuation in dimension to $d=1$ yields a Euclidean version of the BMN matrix quantum mechanics.…
This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time $t$ and conformal time $\eta$ of the Friedmann equations in all dimensions and with an arbitrary cosmological…
The Toda chains take a particular place in the theory of integrable systems, in contrast with the linear group structure for the Gaudin model this system is related to the corresponding Borel group and mediately to the geometry of flag…
We construct SU($N$) super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. It is based on topological field theory formulation for the super Yang-Mills…
This is a survey of the work of Seiberg and Witten on 4-dimensional N=2 supersymmetric Yang-Mills theory and of some of its recent extensions, written for mathematicians. The point of view is that of algebraic geometry and integrable…