Quantum corrections in <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric theories with cubic superpotential,regularized by higher covariant derivatives

Using the higher covariant derivative regularization we calculate a two-loop β-function for the N = 1 supersymmetric Yang-Mills theory with the matter superfields, containing the cubic superpotential. It is found that all integrals, defining this function, are integrals of total derivatives.     

Factorization of Integrals Defining the β-Function into Integrals of Total Derivatives in N=1 SQED, Regularized by Higher Derivatives

Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the β-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics in all orders.     

Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. The text was submitted by the authors in English.     

A new derivation of the Picard-Fuchs equations for effective N = 2 super Yang-Mills theories

A new method to obtain the Picard-Fuchs equations of effective, N = 2 supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding N = 2 theory.     

Structure of the two-point green function of the gauge field for N = 1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives

For the most general renormalizable N = 1 supersymmetric Yang-Mills theory, regularized by higher derivatives, we investigate a contribution to the Gell-Mann-Low function from the two-loop diagrams, containing cubic interaction of the matter superfields. We find that all integrals with respect to the loop momentum in the massless case are factorized to the integrals of total derivatives and can be easily calculated. Thus, we explain the origin of the relation between the two-loop β-function and the one-loop anomalous dimension of the matter superfield.     

Thermodynamic Bethe Ansatz for N = 1 supersymmetric theories

We study a series of N = 1 supersymmetric integrable particle theories in d = 1 + 1 dimensions. These theories are represented as integrable perturbations of specific N = 1 superconformal field theories. Starting from the conjectured S-matrices for these theories, we develop the Thermodynamic Bethe Ansatz (TBA), where we use that the 2-particle S-matrices satisfy a free fermion condition. Our analysis proves a conjecture by E. Melzer, who proposed that these N = 1 supersymmetric. TBA systems are “folded” versions of N = 2 supersymmetric TBA systems that were first studied by P. Fendley and K. Intriligator.     

On the construction of linearized <Emphasis Type="Italic">N</Emphasis> = 1 supergravities coupled to matter

We present a modified formulation of minimal N = 1 linearized supergravity coupled to generic N = 1 supersymmetric matter. The formalism is based on the superprojectors, superspin-transition operators, vector and scalar superfield. Such approach has some advantages for finding superpropagators. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

From 4d superconformal indices to 3d partition functions

An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4d superconformal indices to 3d partition functions which imply an efficient way of getting 3dN=2 supersymmetric dualities for both SYM and CS theories from the “parent” 4dN=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3dN=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter.     

N = 4 supersymmetric quantum mechanics and its large order behaviour

A model of N = 4 supersymmetric quantum mechanics is shown to have a perturbative expansion for which the large order behaviour is - (3/2)ⁿn!(9/π + 5/n + …). In the space of the coupling constants the supersymmetric case is found to be the dividing point between two different types of large order behaviour. In this way the large order behaviour of supersymmetric theories is special.     

A new finite N = 2 supersymmetric sigma model with higher derivatives in four dimensions

A new finite N = 2 supersymmetric sigma model with higher derivatives in four dimensions is formulated. The action of the model is determined in N = 2, d = 4 superspace in terms of N = 2 chiral real superfields. The Lagrangian of the theory under consideration is evaluated in N = 1 super-space and in components. By the methods of N = 2 superfield perturbation theory, it is shown that the constructed N = 2 model is ultraviolet-finite in all orders of quantum perturbation theory in 4-dimensional space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 85–92, April, 1990.     

Thermal spectral functions of strongly coupled N = 4 supersymmetric Yang-Mills theory

We use the gauge-gravity duality conjecture to compute spectral functions of the stress-energy tensor in finite-temperature N = 4 supersymmetric Yang-Mills theory in the limit of large N(c) and large 't Hooft coupling. The spectral functions exhibit peaks characteristic of hydrodynamic modes at small frequency, and oscillations at intermediate frequency. The nonperturbative spectral functions differ qualitatively from those obtained in perturbation theory. The results may prove useful for lattice studies of transport processes in thermal gauge theories.     

Unitarity of rationalN = 2 superconformal theories

We demonstrate that all rational models of theN = 2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu’s algebraA(H₀) (for which we give a physically motivated derivation) explicitly for certain theories, we analyse the modular properties of some of the vacuum characters, and we use the coset realisation of the algebra in terms ofsu(2) and two free fermions. Some of our arguments generalise to the Kazama-Suzuki models indicating that all rationalN = 2 supersymmetric models might be unitary.     

Singlet Deformation of <Emphasis Type="Italic">N</Emphasis> = (1,1) Superspace

We discuss the SO(4) × SU(2) invariant deformation of the Euclidean N = (1,1) supersymmetric theories in the framework of the harmonic superspace.     

The SUSY-QCD <Emphasis Type="Italic">β</Emphasis> function to three loops

A number of [` DR]\overline {\mbox {\textsc{D}R}} renormalization constants in softly broken SUSY- QCD are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts, and ε-scalars, and the renormalization constants for the quark and gluino mass as well as for all cubic vertices. The latter allow us to derive the corresponding β functions through three loops, all of which we find to be identical to the expression for the gauge β function obtained by Jack et al. (Phys. Lett. B 386:138, 1996, ) (see also Pickering et al. in Phys. Lett. B 510, 347, 2001, ). This explicitly demonstrates the consistency of DRED with SUSY and gauge invariance, an important pre-requisite for precision calculations in supersymmetric theories.     

ℵ0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ℵ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories

We study refined and motivic wall-crossing formulas in N=2{{\mathcal N}=2} supersymmetric gauge theories with SU(2) gauge group and N _f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that “refined = motivic.”     

Two-loop iteration of five-point N=4 super-Yang-Mills amplitudes

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin-Barnes representation and the automated package of Czakon [Comput. Phys. Commun. 175, 559 (2006)]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.     

Reflection matrices for integrable N = 1 supersymmetric theories

We study two-dimensional integrable N = 1 supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and we propose exact reflection matrices for the supersymmetric extensions of the multi-component Yang-Lee models and for the breather multiplets of the supersymmetric sine-Gordon theory. We point out the connection between our reflection matrices and the classical boundary actions for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and Zhang [Phys. Lett. B 359 (1995) 118].     

Isolated lepton events at HERA: SUSY R-parity violation?

Events with an isolated high p_T lepton, a hadron jet and missing energy as observed in the H1 experiment at HERA, are potentially associated with R-parity violation in supersymmetric theories. However, stringent kinematic constraints must be fulfilled if the production of supersymmetric particles in R-parity violating scenarios were the correct path for explaining these puzzling events. A reference point ℝ/   is specified for which these constraints are illustrated and implications of the supersymmetric interpretation for new classes of multi-lepton events are indicated.     

On the Complete Classification of Unitary <Emphasis Type="Italic">N</Emphasis> = 2 Minimal Superconformal Field Theories

Aiming at a complete classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric A{\mathcal{A}} -D{\mathcal{D}} -E{\mathcal{E}} models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997).