New avenues in supersymmetry and supergravity

We analyze the problem of constructing supersymmetric versions of gauge theories of particles and of gravity which have a closed supersymmetric algebra. Inparticular we present the basic no-go theorems that indicate that in four dimensions it is not possible to construct suitably extended supersymmetric versions of the above theories without drastic modification of the supersymmetric algebra. Two ways past the“N=3” barrier are discussed; that of central charges involved highly constrained versions which appearn difficult to quantize effectively, while the use of light-cone variables seems to be the most promising. We give light-cone gauge versions of supersymmetric Yang-Mills theories for all extended cases of interest and briefly consider their ultraviolet divergence properties.     

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.     

Supersymmetric Noether Currents and Seiberg–Witten Theory

The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to derive the mass-formula for the quantized Seiberg–Witten model from the supersymmetric algebra. We check that the mass-formula of the low-energy theory agrees with that of the full theory (in the broken phase).     

Supersymmetric lattice theories

We attempt to construct supersymmetric lattice theories using the staggered lattice fermions of Kogut and Susskind. Although we are able to construct lattice field theories with many of the properties of standard supersymmetric models, all of our interacting models violate Lorentz invariance in the continuum limit.     

Instanton effects in supersymmetric theories

We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features.     

On the relation between Green's functions of the SUSY theory with and without soft terms

We study possible relations between the full Green's functions of softly broken supersymmetric theories and the full Green's functions of rigid supersymmetric theories on the example of the supersymmetric quantum mechanics and find that algebraic relations can exist and can be written in a simple form. These algebraic relations between the Green's functions have been derived by transforming the path integral of the rigid theory. In this approach soft terms appear as the result of general changes of coordinates in the superspace.     

Ultraviolet divergences in non-renormalizable supersymmetric theories

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang–Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.     

Anomaly matching conditions in supersymmetric gauge theories

Sufficient conditions are proven for 't Hooft's consistency conditions to hold at points in the moduli space of supersymmetric gauge theories. Known results for anomaly matching in supersymmetric QCD are rederived as a sample application of the results. The results can be used to show that the anomaly matching conditions hold for s-confining theories.     

Regularization by higher derivatives and quantum correction for <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric theories

Some results of regularization by higher covariant derivatives used for investigation of the structure of quantum corrections in N = 1 supersymmetric theories are summarized in the present work. In particular, it is demonstrated that all integrals determining the Hell-Mann-Low functions in supersymmetric theories are integrals of total derivatives. As a consequence, in the N = 1 supersymmetric theories there exists an identity for the Green’s functions which follows from none of the symmetry theories known thus far. The problem of obtaining the exact β-function by the methods of perturbation theory is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 5–35, May, 2008.     

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.     

Quantum phase transitions beyond the Landau-Ginzburg paradigm and supersymmetry

We make connections between studies in the condensed matter literature on quantum phase transitions in square lattice antiferromagnets, and results in the particle theory literature on abelian supersymmetric gauge theories in 2 + 1 dimensions. In particular, we point out that supersymmetric U(1) gauge theories (with particle content similar, but not identical, to those of theories of doped antiferromagnets) provide rigorous examples of quantum phase transitions which do not obey the Landau-Ginzburg-Wilson paradigm (often referred to as transitions realizing “deconfined criticality”). We also make connections between supersymmetric mirror symmetries and condensed matter particle-vortex dualities.     

0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Supersymmetry and functional integration measures

We complete the proof of a recently proposed new characterization of scalar supersymmetric theories and extend this result to “non-scalar” models such as supersymmetric gauge theories. The new characterization does not make use of anticommuting variables since supersymmetry can now be directly understood as a property of certain purely bosonic functional integration measures where all fermionic variables have been “integrated out”.     

Thermodynamic Bethe Ansatz for N = 1 supersymmetric theories

We study a series of N = 1 supersymmetric integrable particle theories in d = 1 + 1 dimensions. These theories are represented as integrable perturbations of specific N = 1 superconformal field theories. Starting from the conjectured S-matrices for these theories, we develop the Thermodynamic Bethe Ansatz (TBA), where we use that the 2-particle S-matrices satisfy a free fermion condition. Our analysis proves a conjecture by E. Melzer, who proposed that these N = 1 supersymmetric. TBA systems are “folded” versions of N = 2 supersymmetric TBA systems that were first studied by P. Fendley and K. Intriligator.     

Quadratic divergences in dimensional-regularization finite quantum field theories

In the search for finite quantum field theories, a set of (supersymmetric as well as non-supersymmetric) models has been singled out by demanding one-loop finiteness in dimensional regularization. We demonstrate that the additional requirement of absence of quadratic divergences provides a clear distinction within this set: only the supersymmetric theories are also free from quadratic divergences whereas the non-supersymmetric models are still quadratically divergent.     

Analysis of the neutralino system in supersymmetric theories

Charginos and neutralinos in supersymmetric theories can be produced copiously at colliders and their properties can be measured with high accuracy. Consecutively to the chargino system, in which the SU(2) gaugino parameter , the higgsino mass parameter and can be determined, the remaining fundamental supersymmetry parameter in the gaugino/higgsino sector of the minimal supersymmetric extension of the Standard Model, the U(1) gaugino mass , can be analyzed in the neutralino system, including its modulus and its phase in CP–noninvariant theories. The CP properties of the neutralino system are characterized by unitarity quadrangles. Analytical solutions for the neutralino mass eigenvalues and the mixing matrix are presented for CP–noninvariant theories in general. They can be written in compact form for large supersymmetric mass parameters. The closure of the neutralino and chargino systems can be studied by exploiting sum rules for the pair-production processes in collisions. Thus the picture of the non–colored gaugino and higgsino complex in supersymmetric theories can comprehensively be reconstructed in these experiments. Received: 24 August 2001 / Published online: 21 November 2001     

Dimensional reduction by legendre transformation generates off-shell supersymmetric Yang-Mills theories

A new technique of dimensional reduction by Legendre transformation to derive off-shell formulations of extended supersymmetric theories is presented. The method starts from an on-shell theory in a higher dimension and retains a dependence of the fields upon one of the higher dimensions, thus allowing for a central charge in the four-dimensional supersymmetry algebra. The “hamiltonian density” of the theory plays the role of the lagrangian in one less dimension, while the equations of motion serve as constraints for the lower dimensional theory. These constraints guarantee supersymmetric and central charge invariances of the action. The technique is applied to derive off-shell formulations of the supersymmetric Yang-Mills theories.     

Supersymmetric nonlinear sigma models constrained on non-compact manifold

A detailed analysis by 1/n expansion is presented of supersymmetric nonlinear sigma models in two dimensions withU(n) symmetry in which the scalar fields are constrained on a non-compact manifold. The theories are ultraviolet finite. In the massless version of the models no mass scale is generated and gauge bosons fail to get dynamics while this is possible provided the theory contains a mass scale. The effects of introduction of the “Ø-term” into supersymmetric theories are also discussed. In particular, it is argued that supersymmetry is broken by the Ø-term only in finite supersymmetric theories. Finally, a singular behavior in the massless limit in these models is pointed out.     

The supersymmetric Adler-Bardeen theorem and regularization by dimensional reduction

We examine the subtraction scheme dependence of the anomaly of the supersymmetric, gauge singlet axial current in pure and coupled supersymmetric Yang-Mills theories. Preserving supersymmetry and gauge invariance explicitly by using supersymmetric background field theory and dimensional reduction, we show that only the one-loop value of the axial anomaly is subtraction scheme independent, and that one can always define a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. In general this subtraction scheme may be non-minimal, but in both the pure and the coupled theories, the Adler-Bardeen theorem is satisfied to two loops in minimal subtraction.     

Multi-Regge form of gluon-exchange amplitudes in supersymmetric Yang-Mills theories

Within supersymmetric Yang-Mills theories, all effective vertices for the interaction of Reggeized gluons with particles were found both in the leading-logarithm approximation and in the next-to-leading-order approximation. The contributions of scalars to the eigenfunction of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel for the adjoint representation of the gauge group and to impact factors similar to those in QCD were calculated. The impact factors that arise in supersymmetric Yang-Mills theories, but which are not present in QCD, are also found. Fulfillment of all bootstrap conditions, which guarantees the multi-Regge form of multiparticle amplitudes in supersymmetric Yang-Mills theories in the next-to-leading-order approximation, was proven. A method for testing bootstrap relations without calculating explicit expressions for vertices and impact factors was developed. This method was used to prove fulfillment of bootstrap conditions in theories featuring any number of fermions and scalar particles transformed according to any representations of the color group and involved in interactions with one another via Yukawa coupling.