Background Superfields Research Articles

One-loop divergences of effective action in 6D, [formula omitted] supersymmetric four-derivative gauge theory

We consider six-dimensional higher-derivative N=(1,0) supersymmetric gauge theory coupled with the hypermultiplet. We use the background superfield method in six-dimensional N=(1,0) harmonic superspace to study the effective action in the theory. Using the dimensional regularization scheme we analyze the one-loop divergent contributions to the effective action. We demonstrate that UV behavior is determined by the higher-derivative term for gauge multiplet sector.

On two-loop divergences of effective action in 6D, mathcal{N} = (1, 1) SYM theory

We study the off-shell structure of the two-loop effective action in 6D, mathcal{N} = (1, 1) supersymmetric gauge theories formulated in mathcal{N} = (1, 0) harmonic superspace. The off-shell effective action involving all fields of 6D, mathcal{N} = (1, 1) supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest mathcal{N} = (1, 0) supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the gauge and the hypermultiplet-mixed divergences as the coefficients of frac{1}{varepsilon^2} and demonstrate that the corresponding expressions are non-local in harmonics.

One-loop divergences in the six-dimensional N=(1,0) hypermultiplet self-coupling model

We study the six-dimensional $\mathcal{N}=(1,0)$ supersymmetric model of the interacting gauge multiplet and hypermultiplet with arbitrary self-coupling. Using the background-field method in the harmonic superspace, we calculate the divergent part of the one-loop effective action and discuss the possible finite contribution to the low-energy effective action. We demonstrate that the one-loop divergences do not vanish even in the case of the on-shell background superfields. An application of the developed technique to the hypermultiplet model in four dimensions is briefly discussed.

On the two-loop divergences in 6D, [formula omitted] SYM theory

We continue studying 6D,N=(1,1) supersymmetric Yang-Mills (SYM) theory in the N=(1,0) harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergences of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs contributing to the effective action, only one diverges off shell. It is also shown that the divergences are proportional to the superfield classical equations of motion and hence vanish on shell. Besides, we have analyzed a possible structure of the two-loop divergences on general gauge and hypermultiplet background.

The renormalization structure of [formula omitted] supersymmetric higher-derivative gauge theory

We consider the harmonic superspace formulation of higher-derivative 6D,N=(1,0) supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives. The theory is quantized in the framework of the superfield background method ensuring manifest 6D,N=(1,0) supersymmetry and the classical gauge invariance of the quantum effective action. We evaluate the superficial degree of divergence and prove it to be independent of the number of loops. Using the regularization by dimensional reduction, we find possible counterterms and show that they can be removed by the coupling constant renormalization for any number of loops, while the divergences in the hypermultiplet sector are absent at all. Assuming that the deviation of the gauge-fixing term from that in the Feynman gauge is small, we explicitly calculate the divergent part of the one-loop effective action in the lowest order in this deviation. In the approximation considered, the result is independent of the gauge-fixing parameter and agrees with the earlier calculation for the theory without a hypermultiplet.

Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, mathcal{N} = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and mathcal{N} = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

Quantum calculation of the low-energy effective action in 5D, [formula omitted] SYM theory

We consider 5D,N=2 supersymmetric Yang-Mills (SYM) theory in 5D,N=1 harmonic superspace as a theory of the interacting adjoint 5D,N=1 gauge multiplet and hypermultiplet. Using the background superfield method, we compute the leading low-energy contribution to the one-loop effective action. The result of quantum calculations precisely matches the effective action derived earlier in arXiv:1812.07206 on the pure symmetry grounds.

On gauge dependence of the one-loop divergences in 6D, [formula omitted] and [formula omitted] SYM theories

We study the gauge dependence of one-loop divergences in a general matter-coupled 6D, N=(1,0) supersymmetric gauge theory in the harmonic superspace formulation. Our analysis is based on the effective action constructed by the background superfield method, with the gauge-fixing term involving one real parameter ξ0. A manifestly gauge invariant and N=(1,0) supersymmetric procedure for calculating the one-loop effective action is developed. It yields the one-loop divergences in an explicit form and allows one to investigate their gauge dependence. As compared to the minimal gauge, ξ0=1, the divergent part of the general-gauge effective action contains a new term depending on ξ0. This term vanishes for the background superfields satisfying the classical equations of motion, so that the S-matrix divergences are gauge-independent. In the case of 6D, N=(1,1) SYM theory we demonstrate that some divergent contributions in the non-minimal gauges do not vanish off shell, as opposed to the minimal gauge.

Supersymmetric DBI equations in diverse dimensions from the BRS invariance of a pure spinor superstring

We examine the BRS invariance of the open pure spinor superstring in the presence of background superfields on a Dp-brane. It is shown that the BRS invariance leads not only to boundary conditions on the spacetime spinors, but also to supersymmetric DBI equations of motion for the background superfields on the Dp-brane. These DBI equations are consistent with the supersymmetric DBI equations for a D9-brane.

Leading low-energy effective action in 6D, mathcal{N}=left(1,1right) SYM theory

We elaborate on the low-energy effective action of 6D, mathcal{N}=left(1,1right) supersymmetric Yang-Mills (SYM) theory in the mathcal{N}=left(1,0right) harmonic superspace formulation. The theory is described in terms of analytic mathcal{N}=left(1,0right) gauge superfield V++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest mathcal{N}=left(1,0right) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N − 1) × ϒ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure sim frac{F^2}{X^2} , where F4 is a monomial of the fourth degree in an abelian field strength FM N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

On the two-loop divergences of the 2-point hypermultiplet supergraphs for 6D, [formula omitted] SYM theory

We consider 6D, N=(1,1) supersymmetric Yang–Mills theory formulated in N=(1,0) harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the N=(1,0) superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.

Shortening anomalies in supersymmetric theories

We present new anomalies in two-dimensional mathcal{N}=left(2,2right) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from mathcal{N}=left(2,2right) spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond mathcal{N}=left(2,2right) . These anomalies explain why the conformal manifolds of the K3 and T4 sigma models are not Kähler and do not factorize into chiral and twisted chiral moduli spaces and why there are no mathcal{N}=left(2,2right) gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.

Two-loop low-energy effective action in Abelian supersymmetric Chern–Simons matter models

We compute two-loop low-energy effective actions in Abelian Chern–Simons matter models with N=2 and N=3 supersymmetry up to four-derivative order. Calculations are performed with a slowly-varying gauge superfield background. Though the gauge superfield propagator depends on the gauge fixing parameter, it is shown that the obtained results are independent of this parameter. In the massless case the considered models are superconformal. We demonstrate that the superconformal symmetry strongly restricts the form of two-loop quantum corrections to the effective actions such that the obtained terms have simpler structure than the analogous ones in the effective action of three-dimensional supersymmetric electrodynamics (SQED) with vanishing topological mass.

Aspects of effective action for super Chern-Simons-Matter models

We develop the superfield background field method and study the effective action in the N = 2, d3 supersymmetric Chern-Simons-matter systems. The one-loop low-energy effective action for non-Abelian supersymmetric Chern-Simons theory is computed to order F4 by use of N = 2 superfield heat kernel techniques.

The background field method for $ \mathcal{N} = {2} $ , d3 super Chern-Simons-matter theories

We develop the superfield background field method and study the effective action in the N=2, d3 supersymmetric Chern-Simons-matter systems. The one-loop low-energy effective action for non-Abelian supersymmetric Chern-Simons theory is computed to order $F^4$ by use of N = 2 superfield heat kernel techniques.

Effective action of three-dimensional extended supersymmetric matter on gauge superfield background

We study the low-energy effective actions for gauge superfields induced by quantum N=2 and N=4 supersymmetric matter fields in three-dimensional Minkowski space. Analyzing the superconformal invariants in the N=2 superspace we propose a general form of the N=2 gauge invariant and superconformal effective action. The leading terms in this action are fixed by the symmetry up to the coefficients while the higher order terms with respect to the Maxwell field strength are found up to one arbitrary function of quasi-primary N=2 superfields constructed from the superfield strength and its covariant spinor derivatives. Then we find this function and the coefficients by direct quantum computations in the N=2 superspace. The effective action of N=4 gauge multiplet is obtained by generalizing the N=2 effective action.

Dynamical breaking of gauge symmetry in supersymmetric quantum electrodynamics in three-dimensional spacetime

The dynamical breaking of gauge symmetry in the supersymmetric quantum electrodynamics in three-dimensional spacetime is studied at two-loop approximation. At this level, the effective superpotential is evaluated in a supersymmetric phase. At one-loop order, we observe a generation of the Chern-Simons term due to a parity violating term present in the classical action. At two-loop order, the scalar background superfield acquires a nonvanishing vacuum expectation value, generating a mass term A{sup {alpha}}A{sub {alpha}} through the Coleman-Weinberg mechanism. It is observed that the mass of gauge superfield is predominantly an effect of the topological Chern-Simons term.

Gauge theory in deformed % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvga % iyaacqWFneVtaaa!4628! $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of $$ \mathcal{N} $$ = (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 $$ \mathcal{N} $$ = (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.

Construction of the effective action in nonanticommutative supersymmetric field theories

We develop a general gauge invariant construction of the one-loop effective action for supersymmetric gauge field theories formulated in N=1/2 superspace. Using manifestly covariant techniques (the background superfield method and proper-time representations) adopted to the N=1/2 superspace we show how to define unambiguously the effective action of a matter multiplet (in fundamental and adjoint representations) and the vector multiplet coupled to a background N=1/2 gauge superfield. As an application of this construction we exactly calculate the low-energy one-loop effective action of matter multiplet and SU(2) SYM theory on the Abelian background.

The solution to Slavnov-Taylor identities in D4 N = 1 SYM

D4 N=1 SYM with an arbitrary chiral background superfield as the gauge coupling is considered. The solution to Slavnov-Taylor identities has been given. It has been shown that the solution is unique and allows us to restrict the gauge part of the effective action. Under the effective action in this paper we mean the 1PI diagram generator.