On A Superfield Extension of The ADHM Construction and N=1 Super Instantons

We give a superfield extension of the ADHM construction for the Euclidean theory obtained by Wick rotation from the Lorentzian four dimensional N=1 super Yang-Mills theory. In particular, we investigate the procedure to guarantee the Wess-Zumino gauge for the superfields obtained by the extended ADHM construction, and show that the known super instanton configurations are correctly obtained.Comment: 22 pages, LaTeX, v2: typos corrected, references adde

Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction

We study an extension of the ADHM construction to give deformed anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n) gauge group. First we extend the exterior algebra on superspace to non(anti)commutative superspace and show that the N=1/2 super Yang-Mills theory can be reformulated in a geometrical way. By using this exterior algebra, we formulate a non(anti)commutative version of the super ADHM construction and show that the curvature two-form superfields obtained by our construction do satisfy the deformed ASD equations and thus we establish the deformed super ADHM construction. We also show that the known deformed U(2) one instanton solution is obtained by this construction.Comment: 32 pages, LaTeX, v2: typos corrected, references adde

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

Master Ward Identity for Nonlocal Symmetries in D=2 Principal Chiral Models

We derive, in path integral approach, the (anomalous) master Ward identity associated with an infinite set of nonlocal conservation laws in two-dimensional principal chiral modelsComment: 12 pages, harvmac, minors correction

Deformations of Lie Algebras using σ\sigma-derivations

In this article we develop an approach to deformations of the Witt and Virasoro algebras based on $\sigma$-derivations. We show that $\sigma$-twisted Jacobi type identity holds for generators of such deformations. For the $\sigma$-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie algebras and their central extensions, which in particular include naturally the $q$-deformations of the Witt and Virasoro algebras associated to $q$-difference operators, providing also corresponding q-deformed Jacobi identities.Comment: 52 page

A Twistor Description of Six-Dimensional N=(1,1) Super Yang-Mills Theory

We present a twistor space that describes super null-lines on six-dimensional N=(1,1) superspace. We then show that there is a one-to-one correspondence between holomorphic vector bundles over this twistor space and solutions to the field equations of N=(1,1) super Yang-Mills theory. Our constructions naturally reduce to those of the twistorial description of maximally supersymmetric Yang-Mills theory in four dimensions.Comment: 15 pages, typos fixed, published versio

Super Multi-Instantons in Conformal Chiral Superspace

We reformulate self-dual supersymmetric theories directly in conformal chiral superspace, where superconformal invariance is manifest. The superspace can be interpreted as the generalization of the usual Atiyah-Drinfel'd-Hitchin-Manin twistors (the quaternionic projective line), the real projective light-cone in six dimensions, or harmonic superspace, but can be reduced immediately to four-dimensional chiral superspace. As an example, we give the 't Hooft and ADHM multi-instanton constructions for self-dual super Yang-Mills theory. In both cases, all the parameters are represented as a single, irreducible, constant tensor.Comment: 21 pg., uuencoded compressed postscript file (twist.ps.Z.uu), other formats (.dvi, .ps, .ps.Z, 8-bit .tex) available at http://insti.physics.sunysb.edu/~siegel/preprints or at ftp://max.physics.sunysb.edu/preprints/siege

Matrix Models and D-branes in Twistor String Theory

We construct two matrix models from twistor string theory: one by dimensional reduction onto a rational curve and another one by introducing noncommutative coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment on the interpretation of our matrix models in terms of topological D-branes and relate them to a recently proposed string field theory. By extending one of the models, we can carry over all the ingredients of the super ADHM construction to a D-brane configuration in the supertwistor space P^(3|4). Eventually, we present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio

Self-Dual N=8 Supergravity as Closed N=2(4) Strings

As open N=2 or 4 strings describe self-dual N=4 super Yang-Mills in 2+2 dimensions, the corresponding closed (heterotic) strings describe self-dual ungauged (gauged) N=8 supergravity. These theories are conveniently formulated in a chiral superspace with general supercoordinate and local OSp(8|2) gauge invariances. The super-light-cone and covariant-component actions are analyzed. Because only half the Lorentz group is gauged, the gravity field equation is just the vanishing of the torsion.Comment: 17 pg., (uuencoded dvi file; revision: forgot 1 stupid term in the last equation) ITP-SB-92-3