We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in Einstein-Maxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known $\mathcal{N} = 2$ supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The $c$-anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
Using Dyson--Schwinger equations within an approach developed by Broadhurst and Kreimer and the renormalization group, we show how high loop order of the renormalization group coefficients can be efficiently computed in a supersymmetric model.
We study the renormalization of an N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is endowed with a foliation structure along a preferred time direction. In curved backgrounds, the target-space geometry is equipped with two distinct metrics, and the interacting sigma model is power-counting renormalizable. At low energies, the theory naturally flows toward the relativistic sigma model where Lorentz symmetry emerges. In the superspace formalism…
We present the full two-loop $β$-functions for the minimal supersymmetric standard model couplings, extended to include R-parity violating couplings through explicit R-parity violation.
Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify the method for the determination of non-supersymmetric counterterms that are needed to maintain supersymmetry.
The conditions for fully supersymmetric backgrounds of general N=2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons te…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to recover gauge invariance, broken by the introduction of the infrared cutoff.
We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein Kähler manifolds are aymptotically free. This result is gerenal and does not depend on the specific forms of the Kähler potentials. We also examine the renormalization group flow in a new model which connects two manifolds with different global symmetries.
We apply the functional renormalization group approach to a $\mathcal{N}=1$ supersymmetric gauge model with one chiral superfield coupled to a vector $U(1)$ superfield. We find that the nonrenormalization theorem still works at leading order in the supercovariant derivative expansion of the fields. We also find the beta functions and we study the behavior of its fixed points in the local potential approximation. Regulators are also discussed.
We provide N=1 Super Yang-Mills theory in the Wess-Zumino gauge with mass terms for the supersymmetric partners of the gauge fields and of the matter fields, together with a supersymmetric mass term for the fermionic matter fields. All mass terms are chosen in such a way to induce soft supersymmetry breakings at most, while preserving gauge invariance to all orders of perturbation theory. The breakings are controlled through an extended Slavnov-Taylor identity. The renormalization analysis, both in the ultraviolet and in the infrared region, is performed.
In this technical note we introduce a manifestly gauge-invariant and supersymmetric procedure to regularize and renormalize one-loop divergences of chiral multiplets in two-dimensional N=(2,2) theories in curved spacetime. We apply the method, a version of Pauli-Villars regularization, to known examples of supersymmetric localization and demonstrate that the partition functions are renormalized. An accompanying ancillary file, a Mathematica notebook, implements the relevant supergravity transformations.
We show that the holomorphic Wilsonian beta-function of a renormalizable asymptotically free supersymmetric gauge theory with an arbitrary semi-simple gauge group, matter content, and renormalizable superpotential is exhausted at 1-loop with no higher loops and no non-perturbative contributions. This is a non-perturbative extension of the well known result of Shifman and Vainshtein.
We present a new real space renormalization-group map, on the space of probabilities, to study the renormalization of the SUSY ϕ^4. In our approach we use the random walk representation on a lattice labeled by an ultrametric space. Our method can be extended to any ϕ^n. New stochastic meaning is given to the parameters involved in the flow of the map and results are provided.
We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N=1 supersymmetric Yang-Mills and show that the local gauge symmetry -broken by the regularization- can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the …
We show how any asymptotically flat supersymmetric solution of minimal d=5 supergravity with flat base space can be deformed into another supersymmetric asymptotically-Godel solution and apply this procedure to the recently found supersymmetric black-ring and black-string solutions.
Some quantum features of vortices in supersymmetric theories in 1+2 dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator…
We give an intuitive proof of a new non-renormalization theorem in supersymmetric field theories. It applies both perturbatively and non-perturbatively. The superpotential is not renormalized in perturbation theory but receives non-perturbative corrections. However, these non-perturbative corrections are {\it not} generic functions of the fields consistent with the symmetries. Certain invariant terms are not generated. This violation of naturalness has applications to dynamical supersymmetry breaking.
The renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking is presented using spurion fields for introducing the breaking terms. It is proven that renormalization of the fields and parameters in the classical action yields precisely the correct counterterms to cancel all divergences. In the course of the construction of higher orders additional independent parameters appear, but they can be shown to be irrelevant in physics respects. Thus, the only parameters with influence on physical amplitudes are the supersymmetric and the well-known soft breaking parameters…
Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking…
The renormalization of the Minimal Supersymmetric Standard Model of electroweak interactions is presented to all orders of perturbation theory using the algebraic method. Special attention is directed to the issues of soft supersymmetry breaking, gauge fixing, and infrared finiteness. We discuss the implications of $\hbar$-dependent field parametrizations on the counterterm structure and provide a complete set of on-shell normalization conditions.
Supersymmetric, asymptotically AdS5, black hole solutions of five dimensional gauged supergravity coupled to arbitrarily many abelian vector multiplets are presented. The general nature of supersymmetric solutions of this theory is discussed. All maximally supersymmetric solutions of this theory (with or without gauging) are obtained.
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings. Indeed, the ordinary renormalization group differential equations can be supplemented with noise, making them into stochastic Langevin equations. Furthermore, if the renormalization group is a gradient flow, the space of couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas. The formulation of the renormalization group as supersymmetric qua…
Using the general results on the classification of timelike supersymmetric solutions of all 4-dimensional N >1 supergravity theories, we show how to construct all the supersymmetric (single- and multi-) black-hole solutions of N=8 supergravity.
Two-loop $β$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the $β$-function appears to be equal to 0, does not depend on the form of regularizing term and does not lead to anomaly puzzle. Two-loop anomalous dimension can be also made independent on parameters of higher derivative regularization by a special choice of subtraction scheme.
Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric Yang-Mills theory, one varies the regularising mass and compensates for it by introducing an effective Wilsonian action. (Polchinski's) Renormalization Group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-function. When supersymmetry is broken up to N=1 the form of effective actions …
We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F^3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F^2 and F^3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F^2 terms to the original lagrangian we render the model renormalizable. We determine the renormalizati…
A new supersymmetric black hole solution of five-dimensional supergravity is presented. It has an event horizon of topology S1xS2. This is the first example of a supersymmetric, asymptotically flat black hole of non-spherical topology. The solution is uniquely specified by its electric charge and two independent angular momenta. These conserved charges can be arbitrarily close, but not exactly equal, to those of a supersymmetric black hole of spherical topology.
We present a minimal version for the renormalization of softly broken Super-Yang-Mills theories using the extended model with a local gauge coupling. It is shown that the non-renormalization theorems of the case with unbroken supersymmetry are valid without modifications and that the renormalization of soft-breaking parameters is completely governed by the renormalization of the supersymmetric parameters. The symmetry identities in the present context are peculiar, since the extended model contains two anomalies: the Adler-Bardeen anomaly of the axial current and an anomaly of supersymmetry in…
The complete renormalization procedure of a general N=1 supersymmetric gauge theory in the Wess-Zumino gauge is presented, using the regulator free ``algebraic renormalization'' procedure. Both gauge invariance and supersymmetry are included into one single BRS invariance. The form of the general nonabelian anomaly is given. Furthermore, it is explained how the gauge BRS and the supersymmetry functional operators can be extracted from the general BRS operator. It is then shown that the supersymmetry operators actually belong to the closed, finite, Wess-Zumino superalgebra when their action is …
We calculate the beta-functions of the general massive (p,q) supersymmetric sigma model to two loop order using (1,0) superfields. The conditions for finiteness are discussed in relation to (p,q) supersymmetry. We also calculate the effective potential using component fields to one loop order and consider the possibility of perturbative breaking of supersymmetry. The effect of one loop finite local counter terms and the ultra-violet behaviour of the off-shell (p,q) models to all orders in perturbation theory are also addressed.
We discus all possible spherically symmetric black hole type solutions to an N=2 supergravity model with SO(3) gauging. The solutions consist of a one parameter family illustrating that the no-hair theorem does not hold and an isolated solution that a supersymmetric analogue of a coloured black hole.
We clarify the mass dependence of the effective prepotential in N=2 supersymmetric SU(N_c) gauge theories with an arbitrary number N_f<2N_c of flavors. The resulting differential equation for the prepotential extends the equations obtained previously for SU(2) and for zero masses. It can be viewed as an exact renormalization group equation for the prepotential, with the beta function given by a modular form. We derive an explicit formula for this modular form when N_f=0, and verify the equation to 2-instanton order in the weak-coupling regime for arbitrary N_f and N_c.
We briefly review the calculations of quantum corrections related with the exact NSVZ $β$-function in ${\cal N}=1$ supersymmetric theories, paying especial attention to the scheme dependence of the results. It is explained, how the NSVZ relation is obtained for the renormalization group functions defined in terms of the bare coupling constant if a theory is regularized by higher derivatives. Also we describe, how to construct a special renormalization prescription which gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactl…
We compute the three loop $β$ function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which works essentially in the physical dimension of the theory we show that ultraviolet are clearly disantangled from infrared divergences. We obtain consistent results which motivate the method as a good choice to study supersymmetry anomalies in quantum field theories.
We renormalize models with scalar chiral superfields with an odd superpotential to several orders in perturbation theory. These extensions of the cubic Wess-Zumino model are renormalizable in spacetime dimensions which are rational. When endowed with an $O(N)$ symmetry it is shown that they share the same property as their non-supersymmetric counterparts in that at a particular fixed point there is an emergent $OSp(1|n-1)$ symmetry, where $n$ is the power of the superpotential. This is shown at a loop order beyond that for which it was established in the parallel non-supersymmetric theory.
Using the Slavnov--Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regularization. Using the restrictions to the renormalization constants which are imposed by the non-renormalization of the considered vertices we express the exact NSVZ $β$-function in terms of the anomalous dimensions of the Faddeev--Popo…
In higher-dimensional Schwarzschild black hole spacetimes, there are no stable bound orbits of particles. In contrast to this, it is shown that there are stable bound orbits in a five-dimensional black lens spacetime.
We present an asymptotically flat supersymmetric black lens solution with the horizon topology L(n,1)=S^3/Z_n in the five-dimensional minimal ungauged supergravity. We show that the black lens carries a mass, two independent angular momenta, electric charge and (n-1) magnetic fluxes, among which only the (n+1) quantities are independent.
For the general renormalizable ${\cal N}=1$ supersymmetric gauge theory we investigate renormalization of the Faddeev--Popov ghosts using the higher covariant derivative regularization. First, we find the two-loop anomalous dimension defined in terms of the bare coupling constant in the general $ξ$-gauge. It is demonstrated that for doing this calculation one should take into account that the quantum gauge superfield is renormalized in a nonlinear way. Next, we obtain the two-loop anomalous dimension of the Faddeev--Popov ghosts defined in terms of the renormalized coupling constant and examin…
This paper shows that the positive-energy and non-renormalization theorems of traditional supersymmetry survive the addition of Lorentz violating interactions. The Lorentz-violating coupling constants in theories using the construction of Berger and Kostelecky must obey certain constraints in order to preserve the positive energy theorem. Seiberg's holomorphic arguments are used to prove that the superpotential remains non-renormalized (perturbatively) in the presence of Lorentz-violating interactions of the Berger-Kostelecky type. We briefly comment on Lorentz-violating theories of the type c…
In this work, we study the nonperturbative renormalization of the supercurrent operator in $\mathcal{N} = 1$ Supersymmetric Yang-Mills (SYM) theory, using a gauge-invariant renormalization scheme (GIRS). The proposed prescription addresses successfully the unwanted mixing of the supercurrent with other operators of equal or lower dimension, which respect the same global symmetries. This mixing is introduced by the unavoidable breaking of supersymmetry on the lattice. In GIRS all gauge-noninvariant operators, which mix with the supercurrent, are excluded from the renormalization procedure. The …
In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of $\,\mathcal{N}=2$ supergravity theories interpolating between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\,\mathcal{N}=8$ supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable ch…
In this work we present an algebraic proof of the renormazibility of the super-Yang-Mills action quantized in a generalized supersymmetric version of the maximal Abelian gauge. The main point stated here is that the generalized gauge depends on a set of infinity gauge parameters in order to take into account all possible composite operators emerging from the dimensionless character of the vector superfield. At the end, after the removal of all ultraviolet divergences, it is possible to specify values to the gauge parameters in order to return to the original supersymmetric maximal Abelian gaug…
The behavior of the beta-function of the low-energy effective coupling in the N=2 supersymmetric SU(2) QCD with several massive matter hypermultiplets and in the SU(3) Yang-Mills theory is determined near the superconformal points in the moduli space. The renormalization group flow is unambiguously fixed by looking at limited types of deformation near the superconformal points. It is pointed out that the scaling dimension of the beta-function is controlled by the scaling behavior of moduli parameters and the relation between them is explicitly worked out. Our scaling dimensions of the beta-fun…
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2+1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the l…
N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kineti…
We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative $β$ functions of these theories are reviewed, and new mechanisms of confinement and dynamical symmetry breaking recently found in a class of $SU(n_c)$, $USp(2n_c)$ and $SO(n_c)$ theories are discussed.
It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of Algebraic Renormalization. We work in the on-shell comp…
We construct a new class of charged, rotating hairy black holes in a consistent truncation of $\mathcal{N} = 8$ supergravity, which retains one charged scalar field and a U$(1)$ gauge field. These hairy solutions can be uplifted to solutions of type IIB supergravity with AdS$_5\times$S$^5$ asymptotics. We find rotating hairy black holes with finite entropy arbitrarily close to the supersymmetric bound - the resulting supersymmetric solution is a one-parameter extension of the Gutowski-Reall solution. These solutions have finite curvature invariants (including at extremality), but in the extrem…
We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens space topology L(2,1). It is the first example of an asymptotically flat black hole with lens space topology. The solution is characterised by a charge, two angular momenta and a magnetic flux through a non-contractible disc region ending on the horizon, with one constraint relating these.
We investigate extremal Reissner-Nordstrom-AdS black holes in four-dimensional N=2 abelian gauged supergravity. We find a new attractor equation which is not reduced to the one in the asymptotically flat spacetime. Focusing on so-called the T^3-model with a single neutral vector multiplet, we obtain non-supersymmetric extremal Reissner-Nordstrom-AdS black hole solutions with regular event horizon in the D0-D4 and the D2-D6 charge configurations. The negative cosmological constant emerges even without the Fayet-Iliopoulos parameters. Furthermore, we also argue the formal description of the non-…
An investigation of the perturbations of the Reissner-Nordström black hole in the $N=2$ supergravity is presented. We prove in the extremal limit that the black hole responds to the perturbation of each field in the same manner. We conjecture that we can match the modes of the graviton, gravitino and photon because of supersymmetry transformations.
The non-renormalization theorem of chiral vertices and the generalized non-renormalization theorem of the photon self energy are derived in SQED on the basis of algebraic renormalization. For this purpose the gauge coupling is extended to an external superfield. This extension already provides detailed insight into the divergence structure. Moreover, using the local supercoupling together with an additional external vector multiplet that couples to the axial current, the model becomes complete in the sense of multiplicative renormalization, with two important implications. First, a Slavnov--Ta…
Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a manifest supersymmetric formulation the anomaly appears in two other identities: The first one describes the non-renormalization of the topological term, the second relates the renormalization of the gauge coupling to the renormalization of the complex supercoupling. Only one of the two identit…
