One-loop renormalisation of N=1/2 supersymmetric gauge theory

We show that N=1/2 supersymmetric gauge theory is renormalisable at one loop, but only after gauge invariance is restored in a non-trivial fashion.Comment: 11 pages, including 3 figures. Plain TeX. Uses Harvmac and epsf. Minor changes and reference adde

Spectral Degeneracy in Supersymmetric Gluodynamics and One-Flavor QCD related to N=1/2 SUSY

In supersymmetric gluodynamics (N=1 super-Yang-Mills theory) we show that the spectral functions induced by the nonchiral operator Tr G_{\alpha\beta} \bar\lambda^2 are fully degenerate in the J^{PC}=1^{\pm -} channels. The above operator is related to N=1/2 generalization of SUSY. Using the planar equivalence, this translates into the statement of degeneracy between the mesons produced from the vacuum by the operators (\bar \Psi \vec E\Psi + i\bar \Psi \vec B \gamma^5\Psi) and (\bar \Psi \vec B\Psi - i\bar \Psi \vec E \gamma^5\Psi) in one-flavor QCD, up to 1/N corrections. Here \Psi is the quark field, and \vec E ,\vec B are chromoelectric/chromomagnetic fields, respectively.Comment: Latex, 6 pages, two references adde

Scalar diagrammatic rules for Born amplitudes in QCD

We show that all Born amplitudes in QCD can be calculated from scalar propagators and a set of three- and four-valent vertices. In particular, our approach includes amplitudes with any number of quark pairs. The quarks may be massless or massive. The proof of the formalism is given entirely within quantum field theory.Comment: 20 pages, references adde

Comments on Gluino Condensates in N=1/2 SYM Theory

Using Ward identities of N=1/2 supersymmetric Yang-Mills theory, we show that while the partition function and antichiral gluino condensates remain invariant under the $C$ deformation, chiral gluino correlators can get contributions from all gauge fields with instanton numbers $k\leq 1$. In particular, a Ward identity of the $U(1)_R$ symmetry allows us to determine the explicit dependence of chiral gluino correlators on the deformation parameter.Comment: 11 pages, 4 figures, small changes, added a referenc

One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model

We discuss the structure of the non-anticommutative N=2 non-linear sigma-model in two dimensions, constructing differential operators which implement the deformed supersymmetry generators and using them to reproduce the classical action. We then compute the one-loop quantum corrections and express them in a more compact form using the differential operators.Comment: 20pp, 8 figures, uses LaTeX. Title expanded to clarify conten

No triangles on the moduli space of maximally supersymmetric gauge theory

Maximally supersymmetric gauge theory in four dimensions has a remarkably simple S-matrix at the origin of its moduli space at both tree and loop level. This leads to the question what, if any, of this structure survives at the complement of this one point. Here this question is studied in detail at one loop for the branch of the moduli space parameterized by a vacuum expectation value for one complex scalar. Motivated by the parallel D-brane picture of spontaneous symmetry breaking a simple relation is demonstrated between the Lagrangian of broken super Yang-Mills theory and that of its higher dimensional unbroken cousin. Using this relation it is proven both through an on- as well as an off-shell method there are no so-called triangle coefficients in the natural basis of one-loop functions at any finite point of the moduli space for the theory under study. The off-shell method yields in addition absence of rational terms in a class of theories on the Coulomb branch which includes the special case of maximal supersymmetry. The results in this article provide direct field theory evidence for a recently proposed exact dual conformal symmetry motivated by the AdS/CFT correspondence.Comment: 39 pages, 4 figure

OPE for Super Loops

We extend the Operator Product Expansion for Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop, dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes.Comment: 16 pages + appendices; 5 figure

The Yangian origin of the Grassmannian integral

In this paper we analyse formulas which reproduce different contributions to scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian integral. Recently their Yangian invariance has been proved directly by using the explicit expression of the Yangian level-one generators. The specific cyclic structure of the form integrated over the Grassmannian enters in a crucial way in demonstrating the symmetry. Here we show that the Yangian symmetry fixes this structure uniquely.Comment: 26 pages. v2: typos corrected, published versio

Inherited Twistor-Space Structure of Gravity Loop Amplitudes

At tree-level, gravity amplitudes are obtainable directly from gauge theory amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We explain how the unitarity method allows us to use these relations to obtain coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes from the recent computation of the coefficients for N=4 super-Yang-Mills non-maximally-helicity-violating amplitudes. We argue from factorisation that these box coefficients determine the one-loop N=8 supergravity amplitudes, although this remains to be proven. We also show that twistor-space properties of the N=8 supergravity amplitudes are inherited from the corresponding properties of N=4 super-Yang-Mills theory. We give a number of examples illustrating these ideas.Comment: 32 pages, minor typos correcte