arXiv subjects

Nikita Nekrasov

Publications and source records attributed to Nikita Nekrasov.

68 records · Page 4Linked to original sources

arXiv1999

Remarks on Covariant Matrix Strings

We address the issue of the worldsheet and spacetime covariant formulation for matrix strings. The problem is solved in the limit of vanishing string coupling. To go beyond the g_s = 0 limit, we propose a topological quantum field theory as a twisted candidate. Our model involves the generalized octonionic or SU(4) instanton equations defined in eight dimensions for a supersymmetric U(N) Yang--Mills field living on a special holonomy manifold. The question of untwisting this matrix model into an anomaly free theory enlightens the need for an "extended" 2d-gravity sector, that we suggest could be (partially twisted) W-gravity.

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arXiv1999

On Non-Supersymmetric CFT in Four Dimensions

We show that the $\mathcal{N}=0$ theories on the self-dual D3-branes of Type 0 string theory are in the class of the previously considered tadpole-free orbifolds of $\mathcal{N} = 4$ theory (although they have SO(6) global symmetry) and hence have vanishing beta function in the planar limit to all orders in 't Hooft coupling. Also, all planar amplitudes in this theory are equal to those of $\mathcal{N} = 4$ theory, up to a rescaling of the coupling.

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arXiv1999

In the Woods of M-Theory

We study BPS states which arise in compactifications of M-theory on Calabi-Yau manifolds. In particular, we are interested in the spectrum of the particles obtained by wrapping M2-brane on a two-cycle in the CY manifold X. We compute the Euler characteristics of the moduli space of genus zero curves which land in a holomorphic four-cycle $S \subset X$. We use M. Kontsevich's method which reduces the problem to summing over trees and observe the discrepancy with the predictions of local mirror symmetry. We then turn this discrepancy into a supporting evidence in favor of existence of extra moduli of M2-branes which consists of the choice of a flat U(1) connection recently suggested by C. Vafa and partially confirm this by counting of the arbitrary genus curves of bi-degree (2,n) in $\IP^1 \times \IP^1$ (this part has been done together with Barak Kol). We also make a conjecture concerning the counting of higher genus curves using second quantized Penner model and discuss possible applications to the string theory of two-dimensional QCD.

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arXiv1998

D-particles, Matrix Integrals and KP hierachy

We study the regularized correlation functions of the light-like coordinate operators in the reduction to zero dimensions of the matrix model describing $D$-particles in four dimensions. We investigate in great detail the related matrix model originally proposed and solved in the planar limit by J. Hoppe. It also gives the solution of the problem of 3-coloring of planar graphs. We find interesting strong/weak 't Hooft coupling dependence. The partition function of the grand canonical ensemble turns out to be a tau-function of KP hierarchy. As an illustration of the method we present a new derivation of the large-N and double-scaling limits of the one-matrix model with cubic potential.

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arXiv1998

Geometric Realizations of BPS States in N=2 Theories

We study the BPS spectrum of the theory on a D3-brane probe in F theory. The BPS states are realized by multi-string configurations in spacetime. Only certain configurations obeying a selection rule give rise to BPS states in the four-dimensional probe theory. Using these string configurations, we determine the spectrum of N=2 SU(2) Yang-Mills. We also explore the relation between multi-string configurations, M theory membranes and self-dual strings.

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arXiv1998

Testing Seiberg-Witten Solution

We propose a few tests of Seiberg-Witten solutions of $\mathcal{N}=2$ supersymmetric gauge theories by the instanton calculus in twisted gauge theories. We re-examine the low-energy effective abelian theory in the presence of sources and present the formalism which makes duality transformations transparent and easily fixes all the contact terms in a broad class of theories. We also discuss ADHM integration and its relevance to the stated problems.

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arXiv1998

Issues in Topological Gauge Theory

We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of sources and study the mixing between the various $p$-observables. We present the twisted superfield formalism which makes duality transformations transparent. We propose a scheme which uniquely fixes all the contact terms. We derive a formula for the correlation functions of $p$-observables on the manifolds of generalized simple type for $0 \leq p \leq 4$ and on some manifolds with $b_{2}^{+} =1$. We study the theories with matter and explore the properties of universal instanton. We also discuss the compactifications of higher dimensional theories. Some relations to sigma models of type $A$ and $B$ are pointed out and exploited.

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arXiv1997

Instanton sums and five-dimensional gauge theories

We analyze the vector multiplet prepotential of d=4, N=2 type IIA compactifications. We find that the worldsheet instanton corrections have a natural interpretation as one-loop corrections in five dimensions, with the extra dimension being compactified on a circle of radius $g_{s}\ell_{s}$. We argue that the relation between spacetime and worldsheet instantons is natural from this point of view. We also discuss the map between the type IIA worldsheet instantons and the spacetime instantons in the heterotic dual.

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arXiv1997

On a Duality in Calogero-Moser-Sutherland Systems

We point out a map between the dynamics of a non-relativistic system of $N$ particles in one dimension interacting via the pair-wise potentials $U_I(q) = (ν^2/4R^2)\sin^2(q/2R)$ and the one of the particles with the pair potential $U_{II}(q) = ν^2/q^2$ and the external potential $U_{ext} = ω^2 q^2/2$. The natural relation between the frequency $ω$ and the radius $R$ is: $ωR = 1$.

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arXiv1997

Five Dimensional Gauge Theories and Relativistic Integrable Systems

We propose a non-perturbative solution of N=2 supersymmetric gauge theory in five dimensions compactified on circle of a radius $R$. We consider the cases of the pure gauge theory as well as the theories with matter in the fundamental and in the adjoint representations. The pure theory as well as the one with adjoint hypermultiplet give rise to the known relativistic integrable systems with ${1\over{R}}$ playing the rôle of the speed of light. The theory with adjoint hypermultiplet exhibits some interesting finiteness properties. Talk given at the III International Conference ``Conformal Field Theories and Integrable Models'', Chernogolovka, June 23-30 1996

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arXiv1996

Chiral Lagrangians, Anomalies, Supersymmetry, and Holomorphy

We investigate higher-dimensional analogues of the $bc$ systems of 2D RCFT. When coupled to gauge fields and Beltrami differentials defining integrable holomorphic structures the $bc$ partition functions can be explicitly evaluated using anomalies and holomorphy. The resulting induced actions generalize the chiral algebras of 2D RCFT to $2n$ dimensions. Moreover, $bc$ systems in four and six dimensions are closely related to supersymmetric matter. In particular, we show that $d=4, \mathcal{N}=2$ hypermultiplets induce a theory of self-dual Yang-Mills fields coupled to self-dual gravity. In this way the $bc$ systems fermionize both the algebraic sector of the $WZW_4$ theory, as defined by Losev et. al., and the classical open $\mathcal{N}_{ws}=2$ string.

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arXiv1995

Holomorphic Bundles and Many-Body Systems

We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion, angle-action variables and quantum systems are discussed. Explicit formulas for the Lax operator on the higher genus surfaces are obtained in the Shottky parameterization. The constructions are motivated by the Conformal Field Theory, and their quantum counterpart can be treated as a degeneration of the critical level Knizhnik-Zamolodchikov-Bernard equations.

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arXiv1994

Relativistic Calogero-Moser model as gauged WZW theory

We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian reduction of integrable systems on the cotangent bundles over semi-simple Lie algebras, their affine algebras and central extensions of loop groups respectively. The corresponding 2d field theories form a tower of deformations. The top of this tower is gauged G/G WZW model on a cylinder with inserted Wilson line in appropriate representation.

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arXiv1994

Elliptic Calogero-Moser system from two dimensional current algebra

We show that elliptic Calogero-Moser system and its Lax operator found by Krichever can be obtained by Hamiltonian reduction from the integrable Hamiltonian system on the cotangent bundle to the central extension of the algebra of SL(N,C) currents.Elliptic deformation of Yang-Mills theory is presented.

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