Reduction of 4-dim self-dual super Yang-Mills equations onto super Riemann surfaces

Recently, a self-dual super Yang-Mills equation over a super Reimann surface was obtained as the zero set of a moment map on the space of superconnections to the dual of the super Lie algebra of gauge transformations. We present a new formulation of the 4-dim Euclidean self-dual super Yang-Mills equations in terms of constraints on the supercurvature. By dimensional reduction, we obtain the same set of superconformal field equations which define self-dual connections on a super Rieman surface.     

Superholomorphic structures,moment maps,and super self-dual Yang-Mills connections over super Riemann surfaces

We consider the space of superconnections with certain curvature constraints over super Riemann surfaces. We define a moment map over that space to the dual of the super Lie algebra of gauge transformations. The zero set of this moment map corresponds to the super self-dual Yang-Mills equations in two dimensions. This result generalizes the recently proposed scheme for the nonsupersymmetric case. The superfield equations also arise from super self-dual Yang-Mills equations in four dimensions by dimensional reduction.     

Higher-Order Inhomogeneous Generalized Heisenberg Supermagnetic Model

We construct the fourth-order inhomogeneous generalized HS model and investigate the integrability property of the supersymmetric integrable system. Moreover, in terms of the gauge transformation, we investigate the corresponding gauge equivalent counterparts under two constraints, i.e., the super inhomogeneous generalized nonlinear Schr?dinger equation and the fermionic inhomogeneous generalized nonlinear Schr?dinger equation.     

Representations of Super Yang-Mills Algebras

We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149–158, 2002), and in fact they appear as a “background independent” formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras ${{\rm {Cliff}}_{q}(k) \otimes A_{p}(k)}$ , for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.     

Beltrami differentials and 2d (super)gravity in the chiral gauge

We consider the Beltrami parametrization of a 2-dimensional metric and work out the basic transformation laws of the constituting fields. These results are then applied to investigate the geometric structure of 2-dimensional gravity in Polyakov's light-cone gauge. Subsequently, we elaborate on the supersymmetric generalization of this theory. The general relation to the superconformai gauge is presented in detail and the corresponding change of coordinates is shown to satisfy simple super Beltrami equations.     

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.     

Superpotentials for Gauge and Conformal Supergravity Backgrounds

Effective superpotentials obtained by integrating out matter in super Yang-Mills and conformal supergravity backgrounds in SUSY theories are considered. The pure gauge and supergravity contributions (generalizing Veneziano-Yankielowicz terms) are derived by considering the case with matter fields in the fundamental representation of the gauge group. These contributions represent quantum corrections to the tree-level Yang-Mills and conformal supergravity actions. The classical equations of motion following from the conformal supergravity action require the background to be (super)conformally flat. This condition is unchanged by quantum corrections to the effective superpotential, irrespective of the matter content of the theory.     

Instanton zero modes and β-functions in gauged supergravity

We prove that one loop infinities in N?3 gauged O(N) supergravities are produced only by zero modes both on de Sitter and gauge instanton backgrounds. This strongly suggests (in analogy with the super Yang-Mills case) that instantons may be used for establishing exact β-functions in supergravities. We also derive the general formula for the number of gauge instanton zero modes for arbitrary spin and find that the “magnetic moment” part of the contribution in the gauge β-function is completely due to zero modes.     

Internal symmetry currents and supersymmetric effective lagrangians

A supersymmetric and non-linearly realized internally symmetric action is constructed from the super Kähler potential of Goldstone scalar superfields. Noether's theorem in superspace is derived and the associated superfield of currents defined. The currents are used to derive a super Dashen formula relating the (quasi) Goldstone masses and decay constants to the symmetry breaking part of the theory and to supersymmetrically gauge the invariant subgroup as well as the full group.     

Superconductivity in Supersymmetric Theory in Restricted Chromodynamics

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N=1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.     

Integrable Deformations of Heisenberg Supermagnetic Model

We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/1）×U（1））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.     

Phase-space Lagrangians for null spinning strings

The striking fact that normal-ordered null strings have the same critical dimension as their usual non-zero tension siblings can be understood from the observation that one must, in the tensionless case, keep all the conjugate momenta as independent dynamical variables, thus doubling the number of physical degrees of freedom. The fermionic momenta give rise to a second-class constraint which cannot be solved covariantly, but can be successfully incorporated into the first-class constraint algebra after gauge-fixing. The ghost contributions to the anomaly consist oftwo b?c (and alsotwo β?γ systems in the supersymmetric case), of the single Virasoro sub(super)algebra for the closed null (spinning) string. In the appropriate gauge, the null (super)string is (super)chiral.     

Expansions of Algebras and Superalgebras and Some Applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the ?nönü–Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).     

Invariants for E0-Semigroups on II1 Factors

We introduce four new cocycle conjugacy invariants for E ₀-semigroups on II ₁ factors: a coupling index, a dimension for the gauge group, a super product system and a C*-semiflow. Using noncommutative Itô integrals we show that the dimension of the gauge group can be computed from the structure of the additive cocycles. We do this for the Clifford flows and even Clifford flows on the hyperfinite II ₁ factor, and for the free flows on the free group factor ${L(F_\infty)}$ L ( F ∞ ) . In all cases the index is 0, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the C*-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate E ₀-semigroups.     

The supersingleton I: Free dipole and interactions at infinity

The program of this Letter, and the one following it, is to develop a formulation of supersymmetric electrodynamics in which the massless fields (photons and neutrinos) are bilinear (actually, commutators) of constituent singleton fields. here we lay the foundations, describing the unique gauge invariant interaction that is allowed in the context of conventional quantum field theory. New quantization rules, leading to super QED, are dealt with in the second Letter.     

Semiclassical gravitoelectromagnetic inflation in a Lorentz gauge: Seminal inflaton fluctuations and electromagnetic fields from a 5D vacuum state

Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. The difference with other previous works is that in this one we use a Lorentz gauge. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of magnetic field modes during the early inflationary epoch of the universe on cosmological scales.     

Second order Hamiltonian formalism and constraints algebra for non-polynomial supergravities

The second order Hamiltonian formalism for a non-polynomial N = 1D = 10 supergravity coupled to super Yang-Mills theory is developed. This is done by starting from the first order canoncial covariant formalism on group manifold. The Hamiltonian, generator of time evolution, is found as a functional of the first class constraints of this coupled system. These contraints close the constraint algebra and they are the generators of all the Hamiltonian gauge symmetries.     

Gauge Theories on ALE Space and Super Liouville Correlation Functions

We present a relation between ${\mathcal{N}=2}$ quiver gauge theories on the ALE space ${\mathcal{O}_{\mathbb{P}^1}(-2)}$ and correlators of ${\mathcal{N}=1}$ super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the ${\mathcal{N}=2^*}$ instanton partition function is given by the product of the character of ${\widehat{SU}(2)_2}$ times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.