super-Weyl Anomalies Research Articles

Non-compact duality, super-Weyl invariance and effective actions

In both mathcal{N} = 1 and mathcal{N} = 2 supersymmetry, it is known that Sp(2n, ℝ) is the maximal duality group of n vector multiplets coupled to chiral scalar multiplets τ(x, θ) that parametrise the Hermitian symmetric space Sp(2n, ℝ)/U(n). If the coupling to τ is introduced for n superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action Γ[τ, overline{tau} ] with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid Sp(2n, ℝ) transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the mathcal{N} = 1 and mathcal{N} = 2 locally supersymmetric “induced actions” which determine the logarithmically divergent parts of the corresponding effective actions. In the mathcal{N} = 1 case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet (n = 1) coupled to a chiral dilaton-axion multiplet. We also describe the general structure of mathcal{N} = 1 super-Weyl anomalies that contain weight-zero chiral scalar multiplets ΦI taking values in a Kähler manifold. Explicit anomaly calculations are carried out in the n = 1 case.

Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization

We present a systematic approach to supersymmetric holographic renormalization for a generic 5D mathcal{N}=2 gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to zero. We determine the complete set of supersymmetric local boundary counterterms, including the finite counterterms that parameterize the choice of supersymmetric renormalization scheme. This allows us to derive holographically the superconformal Ward identities of a 4D superconformal field theory on a generic background, including the Weyl and super-Weyl anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a conformal Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a conformal Killing spinor.

Super-Weyl anomalies in $ \mathcal{N} $ = 2 supergravity and (non)local effective actions

Using the formulation for N=2 conformal supergravity in SU(2) superspace, we define super-Weyl (or superconformal) anomalies and construct two types of nonlocal effective actions that generate these anomalies. We also present the local Wess-Zumino action for spontaneously broken N=2 superconformal symmetry, with the Goldstone supermultiplet identified with a reduced chiral superfield containing the dilaton and the axion among its components.

Nonlocal action for the super-Weyl anomalies: a new representation

Using the recently discovered N=1 supersymmetric extension of the conformal fourth-order scalar operator (introduced originally by Fradkin and Tseytlin and also known as the "Paneitz operator" or "Riegert operator"), we derive a new representation for the nonlocal action generating the super-Weyl anomalies.

Gauge threshold corrections for local string models

We study gauge threshold corrections for local brane models embedded in a large compact space. A large bulk volume gives important contributions to the Konishi and super-Weyl anomalies and the effective field theory analysis implies the unification scale should be enhanced in a model-independent way from M_s to R M_s. For local D3/D3 models this result is supported by the explicit string computations. In this case the scale R M_s comes from the necessity of global cancellation of RR tadpoles sourced by the local model. We also study D3/D7 models and discuss discrepancies with the effective field theory analysis. We comment on phenomenological implications for gauge coupling unification and for the GUT scale.

Field dependent gauge couplings in locally supersymmetric effective quantum field theories

We investigate the field dependence of the gauge couplings of locally supersymmetric effective quantum field theories. We find that the Weyl rescaling of supergravity gives rise to Wess-Zumino terms that affect the gauge couplings at the one-loop level. These Wess-Zumino terms are crucial in assuring supersymmetric consistency of both perturbative and non-perturbative gauge interactions. At the perturbative level, we distinguish between the holomorphic wilsonian gauge couplings and the physically-measurable momentum-dependent effective gauge couplings; the latter are affected by the Konishi and the super-Weyl anomalies and their field-dependence is non-holomorphic. At the non-perturbative level, we show how consistency of the scalar potential generated by infrared-strong gauge interactions with the local supersymmetry requires a very specific form of the effective superpotential. We use this superpotential to determine the dependence of the supersymmetric condensates of a strongly interacting gauge theory on its (field-dependent) wilsonian gauge coupling and the Yukawa couplings of the matter fields. The article concludes with the discussion of the field-dependent non-perturbative phenomena in the context of string unification.

Consistent Fujikawa regularization of the spinning string in superspace from Pauli-Villars regularization.

We use Pauli-Villars (PV) regularization of the spinning string in superspace to identify those Fujikawa regulators which produce consistent anomalies. We use a general background gauge, and obtain, after elimination of the nonpropagating fields and using a super-Einstein and Lorentz-invariant mass term, a diagonal Fujikawa regulator with only super-Weyl anomalies. The PV extended action has extra twisted'' Becchi-Rouet-Stora-Tyutin (BRST) symmetries; dropping these, the BRST transformations of the PV fields turn into off-shell superconformal transformations plus field equations. Thus, the transformations of superconformal field theory are just on-shell BRST transformations.

Topological approach to Weyl and super-Weyl anomalies in string theory.

Cohomological methods are used to determine the functional form of the Weyl and super-Weyl anomalies in the bosonic and heterotic strings. The Wess-Zumino terms associated with these anomalies are calculated. The super-Weyl anomaly is discussed within the context of the (1,0) superspace formalism.

Topology and heterotic, gravitational, Lorentz and super-Weyl anomalies

The (1,0) superdiffeomorphic and Lorentz anomalies are constructed using cohomology and descent equations in heterotic superspace. The superfield gravitational Wess-Zumino term is presented. Supergraph techniques are used to calculate the coefficients of the superdiffeomorphic, Lorentz and super-Weyl anomalies.

Schwinger terms of the super-Virasoro algebra in (1,0) superspace.

We calculate the Schwinger terms of the super-Virasoro algebra for the heterotic string, and the associated anomalous seagull terms, directly from the Lorentz and super-Weyl anomalies using the (1,0) superspace formalism. The various supercurrents in (1,0) superspace are also discussed.

The relationship between the canonical super-virasoro and functional super-Weyl anomalies

In this letter, recent work relating the various anomalies encountered in the different quantisation approaches, is extended to the superstring. The reparametrization and supersymmetry anomalies of the canonical approach are constructed from the super-Weyl anomaly of the path-integral approach via the descent equations. We also give an exact correspondence between this procedure and operations in canonical field theory.

(1, 0) Supergravity

We discuss the quantization of two-dimensional (1, 0) superfields and the background field formalism for (1, 0) supergravity. As an application we compute the supergravitational and super-Weyl anomalies of ( p, q)-type string actions and determine the corresponding critical dimensions. We also compute the ghost supercurrent anomalies for the general first-order ghost action.

Heterotic-string anomalies in (1,0) superspace

The supergravitational and super-Weyl anomalies of the heterotic string are computed using the background field method for (1,0) superfield supergravity. The cancellation, at the critical dimension, of the full super-Weyl anomaly is an automatic consequence of our supergraph calculation. The (1,0) superfield action is also given for the “bosonic formulation” of the heterotic string.

Cohomologies and anomalies in supersymmetric theories

We analyze the anomaly structure of renormalizable supersymmetric models coupled to supergravity using cohomological methods. We study the cohomology corresponding to superdiffeomorphisms, superlocal Lorentz and super-Weyl transformations. We conclude that in four dimensions superdiffeomorphisms and Lorentz transformations are anomaly free for all the models of interest. We determine the superWeyl anomalies.