Supersymmetry anomalies and some aspects of renormalization

We show how the $\text{L}$-matrix elements avoid the problem of supersymmetry breaking by the gauge fixing and ghost terms for renormalization in the Wess-Zumino gauge. Possible origins of supersymmetry anomalies are discussed. Gauge and gravitational anomalies induce a supersymmetry anomaly which has two distinct terms, one of which is gauge invariant. We give the expression for the noninvariant term for 2n-dimensional spacetime and for the invariant part in four dimensions. This anomaly, although cohomologically nontrivial, is still consistent with result that in superspace no supersymmetry anomaly is generated.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

Supersymmetry anomally in two dimensions

In two dimensions we obtain a supersymmetric extension of a gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We also obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies.     

Coupled chiral and supersymmetry anomalies in supersymmetric Yang-Mills theories

Supersymmetric Yang—Mills theories in component formulation lead to coupled chiral and supersymmetry anomalies. In ten dimensions the coupled consistency conditions are solved to give the lending term for the supersymmetry anomaly.     

Anomaly cancellations in the local supersymmetric Siegel lagrangian

The local supersymmetric Siegel action for two-dimensional chiral bosons and fermions is studied. It is found that the theory has local supersymmetry anomalies as well as gravitational-like anomalies. A modification of the lagrangian yielding anomaly cancellations is obtained.     

Topological anomalies from the path integral measure in superspace

A fully quantum version of the Witten-Olive analysis of the central charge in the N=1 Wess-Zumino model in d=2 with a kink solution is presented by using path integrals in superspace. We regulate the Jacobians with heat kernels in superspace, and obtain all superconformal anomalies as one Jacobian factor. The conserved quantum currents differ from the Noether currents by terms proportional to field equations, and these terms contribute to the anomalies. We identify the particular variation of the superfield which produces the central charge current and its anomaly; it is the variation of the auxiliary field. The quantum supersymmetry algebra which includes the contributions of superconformal anomalies is derived by using the Bjorken-Johnson-Low method instead of semi-classical Dirac brackets. We confirm earlier results that the BPS bound remains saturated at the quantum level due to equal anomalies in the energy and central charge.     

(2, 0) supersymmetry and space-time supersymmetry in the heterotic string theory

Criteria for unbroken N=1 space-time supersymmetry in the heterotic string theory in the presence of background fields are discussed. We make use of the construction of the fermion vertex operator in the Neveu-Schwarz-Ramond model. (2, 0) world-sheet supersymmetry is shown to be one of the necessary conditions for space-time supersymmetry in most cases. Constraints on the various background fields implied by (2, 0) world-sheet supersymmetry are derived, taking into account the effect of σ-model loop corrections. Special care is taken to study the effect of local Lorents and gauge anomaly on these constraints. Our analysis determines the constraints unambigously up to field redefinitions.     

Superconformal anomalies and the effective lagrangian for pure supersymmetric QCD

We discuss the extent to which the superconformal anomalies constrain the effective lagrangian for pure N = 1 Yang-Mills theory. Assuming that the order parameter describing the model is a single chiral superfield (and allowing its derivatives) we find a larger class of possible models than had been previously noted. We give a detailed analysis of a particularly interesting example and find that it leads to the possibility of spontaneous breakdown of supersymmetry. Thus we conclude that the anomaly constraints by themselves are not sufficient to protect supersymmetry. Some unusual features which seem characteristic of such higher derivative theories are noted. A number of related topics, including the question of gluon condensation, are discussed.     

Dynamical supersymmetry breaking in two-dimensional N = 1 supergravity theories

We investigate a possible dynamical mechanism for spontaneous supersymmetrybreaking in N = 1 supergravity theories in 1 + 1 space-time dimensions. It will be shown that supersymmetry is never broken at the tree level, but it can be broken for a certain class of models by quantum effects due to trace anomalies of the energy-momentum tensor and the supercurrent.     

Anomalies,ambiguities and superstrings

It is shown that anomalies only change trivially if a covariant term is added to the gauge connection. As a result, for the superstring, the anomalies can be cancelled if the anti-symmetric tensor field strength H is modified by the Chern-Simons form of any spin-connection, possibly with torsion. The low-energy effective field theory is, then, not uniquely determined by requiring anomaly cancellation and supersymmetry. Implications for string compactifications are considered.     

Homology of Lie algebra of supersymmetries and of super Poincaré Lie algebra

We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincaré Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions ?11. For dimensions D=10,11 we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry Lie algebras.     

Solving central charge constraints in extended super-Yang-Mills theories

We obtain a local lagrangian involving unconstrained fields for the N = 2 and 4 non-abelian super-Yang-Mills in the central charge version obtained by dimensional reduction by Legendre transformation from five dimensions. The resulting Lorentz and supersymmetry transformations do possess non-locality, however.     

R4 couplings in M- and type II theories on Calabi-Yau spaces

We discuss several implications of R⁴ couplings in M-theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chem-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N = 2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type 11 string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.     

Consistency condition calculations of supersymmetry anomalies

Using differential geometry in superspace it is shown how consistency conditions are solved for coupled supersymmetry, gauge and Lorentz anomalies in normal space-time. Anomaly cancellation mechanisms in d = 10 are shown to remove possible supersymmetry anomalies as well as gauge and Lorentz anomalies.     

Special geometry in hypermultiplets

We give a detailed analysis of pairs of vector and hypermultiplet theories with N = 2 supersymmetry in four space-time dimensions that are related by the (classical) mirror map. The symplectic reparametrizations of the special Kähler space associated with the vector multiplets induce corresponding transformations on the hypermultiplets. We construct the Sp(1) × Sp(n) one-forms in terms of which the hypermultiplet couplings are encoded and exhibit their behaviour under symplectic reparametrizations. Both vector and hypermultiplet theories allow vectorial central charges in the supersymmetry algebra associated with integrals over the Kähler and hyper-Kähler forms, respectively. We show how these charges and the holomorphic BPS mass are related by the mirror map.     

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CP^N?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CP^N?1 model thus obtained admits an O(2) extended supersymmetry.     

Absence of hexagon gauge anomalies in higher loop superstring amplitudes

It is shown that there are no gravitational, Yang-Mills, local supersymmetry hexagon anomalies in higher genus amplitudes of type II superstring and heterotic string theory in ten dimensions. The nonrenormalization theorem for massless parity-violating higher genus amplitudes is also proved.     

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.     

Can supersymmetric theories be bosonized?

We investigate the possibility of transforming supersymmetric theories into pure;y fermionic or bosonic forms. The supersymmetric sine-Gordon lagrangian is rewritten in a purely fermionic form, and the Fermi equivalent of the original supersymmetry transformation is derived. This transformation represents an invariance only at the quantum level, when the effects of the chiral anomaly have been taken into account. When supersymmetric theories are written in purely bosonic forms, a non-local bosonic transformation takes place of the supersymmetry transformation. In both cases the supersymmetry algebra, as realized on the fields, is lost.     

Gravitational anomalies

The effective action for fermions moving in external gravitational and gauge fields is analyzed in terms of the corresponding external field propagator. The central object in our approach is the covariant energy-momentum tensor which is extracted from the regular part of the propagator at short distances. It is shown that the Lorentz anomaly, the conformal anomaly and the gauge anomaly can be expressed in terms of the local polynomials which determine the singular part of the propagator. (There are no coordinate anomalies.) Except for the conformal anomaly, for which we give explicit representations only ind<=4, we consider an arbitrary number of dimensions.