Superconformal Anomaly Research Articles

Corrections to AdS5 black hole thermodynamics from higher-derivative supergravity

We study four-derivative corrections to five-dimensional minimal gauged supergravity. We evaluate the on-shell action of the AdS5 black hole solution with two independent angular momenta and one electric charge at linear order in the corrections. After imposing supersymmetry, we are able to recast the action in terms of the supersymmetric chemical potentials and match the result obtained from the dual superconformal index on the second sheet. To achieve this, we exploit the freedom to implement field redefinitions to recast the action in a much simpler form, as well as the fact that the two-derivative solution is enough. We use the on-shell action to determine the corrections to the black hole thermodynamics, including those to the entropy and the charges. We then specialize to the supersymmetric and extremal case and find a simple expression for the microcanonical entropy. In particular, for the case with one independent angular momentum the corrections are entirely encoded in the dual superconformal anomaly coefficients. We corroborate this result for the entropy by constructing the corrected near-horizon solution and applying Wald’s formula.

The three-loop MHV octagon from overline{Q} equations

The overline{Q} equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar mathcal{N} = 4 supersymmetric Yang-Mills theory. By using the overline{Q} equations, we compute the symbol of the first MHV amplitude with algebraic letters — the three-loop 8-point amplitude (or the octagon remainder function) — in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

Trace and Axial Anomalies on Equal Footing

We discussed that for some particular nonsupersymmetric theories, a generalized symmetry that includes both the scale and axial transformations and leads to a single current may contain also a pseudoscalar term. The method, inspired by the superconformal anomalies, has important application for low-energy effective models where it allows the introduction of a single complex glueball field with a scalar and a pseudoscalar component on the same footing with the complex meson nonet fields made of quarks. Both axial and trace anomalies are satisfied in accordance to the meson structure and the QCD requirements.

Supersymmetry anomalies in mathcal{N}=1 conformal supergravity

We solve the Wess-Zumino consistency conditions of mathcal{N}=1 off-shell conformal supergravity in four dimensions and determine the general form of the superconformal anomalies for arbitrary a and c anomaly coefficients to leading non trivial order in the gravitino. Besides the well known Weyl and R-symmetry anomalies, we compute explicitly the fermionic mathcal{Q} - and mathcal{S} -supersymmetry anomalies. In particular, we show that mathcal{Q} -supersymmetry is anomalous if and only if R-symmetry is anomalous. The mathcal{Q} - and mathcal{S} -supersymmetry anomalies give rise to an anomalous supersymmetry transformation for the supercurrent on curved backgrounds admitting Killing spinors, resulting in a deformed rigid supersymmetry algebra. Our results may have implications for supersymmetric localization and supersymmetry phenomenology. Analogous results are expected to hold in dimensions two and six and for other supergravity theories. The present analysis of the Wess-Zumino consistency conditions reproduces the holographic result of arXiv:1703.0429 and generalizes it to arbitrary a and c anomaly coefficients.

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F-theorem and possibly a C-theorem in five-dimensional superconformal theories.

Supercurrent anomalies in 4d SCFTs

We use holographic renormalization of minimal mathcal{N}=2 gauged supergravity in order to derive the general form of the quantum Ward identities for 3d mathcal{N}=2 and 4d mathcal{N}=1 superconformal theories on general curved backgrounds, including an arbitrary fermionic source for the supercurrent. The Ward identities for 4d mathcal{N}=1 theories contain both bosonic and fermionic global anomalies, which we determine explicitly up to quadratic order in the supercurrent source. The Ward identities we derive apply to any superconformal theory, independently of whether it admits a holographic dual, except for the specific values of the a and c anomaly coefficients, which are equal due to our starting point of a two-derivative bulk supergravity theory. We show that the fermionic anomalies lead to an anomalous transformation of the supercurrent under rigid supersymmetry on backgrounds admitting Killing spinors, even if all superconformal anomalies are numerically zero on such backgrounds. The anomalous transformation of the supercurrent under rigid supersymmetry leads to an obstruction to the Q-exactness of the stress tensor in supersymmetric vacua, and may have implications for the applicability of localization techniques. We use this obstruction to the Q-exactness of the stress tensor, together with the Ward identities, in order to determine the general form of the stress tensor and R-current one-point functions in supersymmetric vacua, which allows us to obtain general expressions for the supersymmetric Casimir charges and partition function.

Supersymmetry on curved spaces and superconformal anomalies

We study the consequences of unbroken rigid supersymmetry of four-dimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the R-current is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite R-charge are preserved, otherwise the (anti-)self-dual part of the vector field-strength is fixed by the Weyl tensor. As a result of this relation, the trace and R-current anomalies of superconformal field theories simplify, with the trace anomaly becoming purely topological. In particular, in Lorentzian signature, or in the presence of two Euclidean supercharges of opposite R-charge, supersymmetry of the background implies that the term proportional to the central charge c vanishes, both in the trace and R-current anomalies. This is equivalent to the vanishing of a superspace Weyl invariant. We comment on the implications of our results for holography.

SUPERGRAVITY DUAL OF THE SUPERCONFORMAL ANOMALY

The supergravity dual of the superconformal anomaly multiplet in a four-dimensional supersymmetric gauge theory is investigated. We consider a well-established dual correspondence between an [Formula: see text]SU(N+M) × SU(N) supersymmetric gauge theory and type IIB superstring in a space–time background described by the Klebanov–Strassler solution. Based on the fact that fractional D3-branes lead to superconformal anomaly on the field theory side and in the meantime deform AdS 5 × T1, 1 space–time background on the gravity side, we observe the five-dimensional gauged supergravity yielded from the spontaneous compactification on the deformed T1, 1, and find that the spontaneous breaking of local symmetries and the consequent super-Higgs effect in the gauged AdS5 supergravity should be the dual of the superconformal anomaly of the four-dimensional supersymmetric gauge theory.

Goldstinos, supercurrents and metastable SUSY breaking in $ \mathcal{N} = 2 $ supersymmetric gauge theories

We construct an N=2 supersymmetric generalization of the N=1 supercurrent formalism of Komargodski and Seiberg (KS) and use it to show that N=2 theories with linear superconformal anomalies cannot break SUSY under certain broad assumptions. This result suggests that there are no metastable SUSY breaking vacua in a large class of theories that includes N=2 Super Yang-Mills (SYM).

One-loop superconformal and Yangian symmetries of scattering amplitudes in $$ \mathcal{N} = 4 $$ super Yang-Mills

Recently it has been argued that tree-level scattering amplitudes in N=4 Yang-Mills theory are uniquely determined by a careful study of their superconformal and Yangian symmetries. However, at one-loop order these symmetries are known to become anomalous due to infrared divergences. We compute these one-loop anomalies for amplitudes defined through dimensional regularisation by studying the tree-level symmetry transformations of the unitarity branch cuts, keeping track of the crucial collinear terms arising from the holomorphic anomaly. We extract the superconformal anomalies and show that they may be cancelled through a universal one-loop deformation of the tree-level symmetry generators which involves only tree-level data. Specialising to the planar theory we also obtain the analogous deformation for the level-one Yangian generator of momentum. Explicit checks of our one-loop deformation are performed for MHV and the 6-point NMHV amplitudes.

Anomaly-mediated supersymmetry breaking demystified

We reinterpret anomaly-mediated supersymmetry breaking from a field-theoretic perspective in which superconformal anomalies couple to either the chiral compensator or the $U(1)_R$ vector superfield. As supersymmetry in the hidden sector is spontaneously broken by non-vanishing vacuum expectation values of the chiral compensator F-term and/or the $U(1)_R$ vector superfield D-term, the soft breakdown of supersymmetry emerges in the visible sector. This approach is physically more understandable compared with the conventional approach where the chiral compensator is treated on the same footing as a spurion in gauge-mediated supersymmetry breaking scenario.

Seesaw extended MSSM and anomaly mediation without tachyonic sleptons

Superconformal anomalies provide an elegant and economical way to understand the soft breaking parameters in SUSY models; however, implementing them leads to the several undesirable features including: tachyonic sleptons and electroweak symmetry breaking problems in both the MSSM and the NMSSM. Since these two theories also have the additonal problem of massless neutrinos, we have reconsidered the AMSB problems in a class of models that extends the NMSSM to explain small neutrino masses via the seesaw mechanism. In a recent paper, we showed that for a class of minimal left-right extensions, a built-in mechanism exists which naturally solves the tachyonic slepton problem and provides new alternatives to the MSSM that also have automatic R-parity conservation. In this paper, we discuss how electroweak symmetry breaking arises in this model through an NMSSM-like low energy theory with a singlet VEV, induced by the structure of the left-right extension and of the right magnitude. We then study the phenomenological issues and find: the LSP is an Higgsino-wino mix, new phenomenology for chargino decays to the LSP, degenerate same generation sleptons and a potential for a mild squark-slepton degeneracy. We also discuss possible collider signatures and the feasibility of dark matter in this model.

Central charge anomalies in 2D sigma models with twisted mass

We discuss the central charge in supersymmetric ${\cal N}=2$ sigma models in two dimensions. The target space is a symmetric K\"ahler manifold, CP$(N-1)$ is an example. The U(1) isometries allow one to introduce twisted masses in the model. At the classical level the central charge contains Noether charges of the U(1) isometries and a topological charge which is an integral of a total derivative of the Killing potentials. At the quantum level the topological part of the central charge acquires anomalous terms. A bifermion term was found previously, using supersymmetry which relates it to the superconformal anomaly. We present a direct calculation of this term using a number of regularizations. We derive, for the first time, the bosonic part in the central charge anomaly. We construct the supermultiplet of all anomalies and present its superfield description. We also discuss a related issue of BPS solitons in the CP(1) model and present an explicit form for the curve of marginal stability.

Derivation of Superconformal Anomaly without Ghosts in N = 1 SYM4

The anomalous Ward-Takahashi identity for the superconformal symmetry in the four-dimensional N = 1 supersymmetric Yang-Mills theory is studied in terms of the stochastic quantization method (SQM). By applying the background field method to the SQM approach, we derive the superconformal anomaly in the one-loop approximation and show that the supersymmetric stochastic gauge fixing term does not contribute to the anomaly.

Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories

The effect of quantum fluctuations on Bogomol'nyi-Prasad-Sommerfield (BPS)-saturated topological excitations in supersymmetric theories is studied. Focus is placed on a sequence of topological excitations that derive from the same classical soliton or vortex in lower dimensions and it is shown that their quantum characteristics, such as the spectrum and profile, differ critically with the dimension of spacetime. In all the examples examined the supercharge algebra retains its classical form although short-wavelength fluctuations may modify the operator structure of the central charge, yielding an anomaly. The central charge, when the expectation value is taken, is further affected by long-wavelength fluctuations, and this makes the BPS-excitation spectra only approximately calculable in some low-dimensional theories. In four dimensions, in contrast, holomorphy plays a special role in stabilizing the BPS-excitation spectra against quantum corrections. The basic tool in our study is the superfield supercurrent, from which the supercharge algebra with a central extension is extracted in a supersymmetric setting. A general method is developed to determine the associated superconformal anomaly by considering dilatation directly in superspace.

Phenomenological aspects of heterotic orbifold models at one loop

We provide a detailed study of the phenomenology of orbifold compactifications of the heterotic string within the context of supergravity effective theories. Our investigation focuses on those models where the soft Lagrangian is dominated by loop contributions to the various soft supersymmetry breaking parameters. Such models typically predict non-universal soft masses and are thus significantly different from minimal supergravity and other universal models. We consider the pattern of masses that are governed by these soft terms and investigate the implications of certain indirect constraints on supersymmetric models, such as flavor-changing neutral currents, the anomalous magnetic moment of the muon and the density of thermal relic neutralinos. We also comment on the possible discovery of these models at the LHC. These string-motivated models show a novel behavior that interpolates between the phenomenology of unified supergravity models and models dominated by the superconformal anomaly.

Electroweak symmetry breaking via UV insensitive anomaly mediation

Anomaly mediation solves the supersymmetric flavor and CP problems. This is because the superconformal anomaly dictates that supersymmetry breaking is transmitted through nearly flavor-blind infrared physics that is highly predictive and UV insensitive. Slepton mass squareds, however, are predicted to be negative. This can be solved by adding D-terms for U(1)_Y and U(1)_{B-L} while retaining the UV insensitivity. In this paper we consider electroweak symmetry breaking via UV insensitive anomaly mediation in several models. For the MSSM we find a stable vacuum when tanbeta < 1, but in this region the top Yukawa coupling blows up only slightly above the supersymmetry breaking scale. For the NMSSM, we find a stable electroweak breaking vacuum but with a chargino that is too light. Replacing the cubic singlet term in the NMSSM superpotential with a term linear in the singlet we find a stable vacuum and viable spectrum. Most of the parameter region with correct vacua requires a large superpotential coupling, precisely what is expected in the ``Fat Higgs'' model in which the superpotential is generated dynamically. We have therefore found the first viable UV complete, UV insensitive supersymmetry breaking model that solves the flavor and CP problems automatically: the Fat Higgs model with UV insensitive anomaly mediation. Moreover, the cosmological gravitino problem is naturally solved, opening up the possibility of realistic thermal leptogenesis.

Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with $N=1$ supersymmetry. Extensive use is made of the superfield supercurrent that places the supercurrent ${J}_{\ensuremath{\alpha}}^{\ensuremath{\mu}},$ energy-momentum tensor ${\ensuremath{\Theta}}^{\ensuremath{\mu}\ensuremath{\nu}},$ and topological current ${\ensuremath{\zeta}}^{\ensuremath{\mu}}$ in a supermultiplet to study the structure of supersymmetry and related superconformal symmetry in the presence of solitons. It is shown that the supermultiplet structure of ${(J}_{\ensuremath{\alpha}}^{\ensuremath{\mu}},{\ensuremath{\Theta}}^{\ensuremath{\mu}\ensuremath{\nu}},{\ensuremath{\zeta}}^{\ensuremath{\mu}})$ is kept exact while the topological current ${\ensuremath{\zeta}}^{\ensuremath{\mu}}$ acquires a quantum modification through the superconformal anomaly. In addition, the one-loop superfield effective action is explicitly constructed to verify the BPS saturation of the soliton spectrum as well as the effect of the anomaly.

Derivation of the Superconformal Anomaly without Ghosts in N=1 SYM_4

Derivation of the Superconformal Anomaly without Ghosts in N=1 SYM_4

The holographic supercurrent anomaly

The γ-trace anomaly of supersymmetry current in a supersymmetric gauge theory shares a superconformal anomaly multiplet with the chiral R-symmetry anomaly and the Weyl anomaly, and its holographic reproduction is a valuable test to the AdS/CFT correspondence conjecture. We investigate how the γ-trace anomaly of the supersymmetry current of N=1 four-dimensional supersymmetric gauge theory in an N=1 conformal supergravity background can be extracted out from the N=2 gauged supergravity in five dimensions. It is shown that the reproduction of this super-Weyl anomaly originates from the following two facts: first the N=2 bulk supersymmetry transformation converts into N=1 superconformal transformation on the boundary, which consists of N=1 supersymmetry transformation and special conformal supersymmetry (or super-Weyl) transformation; second the supersymmetry variation of the bulk action of five-dimensional gauged supergravity is a total derivative. The non-compatibility of supersymmetry and the super-Weyl transformation invariance yields the holographic supersymmetry current anomaly. Furthermore, we speculate on that the contribution from the external gauge and gravitational background fields to the superconformal anomaly may have different holographic origin.