Coupling supersymmetric Yang-Mills theories to supergravity

We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace $\text{M}{}^2\text{= Σ}{}_{\mathrm{J}}\text{(?)}{}^{\mathrm{2J}}\text{(2J + 1)m}{}_{\mathrm{J}}{}^2\text{= 2(N ? 1)m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^2$, where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.     

Perturbation theory and renormalization of supersymmetric Yang-Mills theories

We solve the problem of introducing, in supersymmetric Yang-Mills Lagrangians, a supersymmetric gauge breaking term and a Faddeev-Popov ghost interaction term. The resulting Lagrangian turns out to be invariant under a global symmetry transformation which is the supersymmetric extension of the Slavnov symmetry. We show that the complete analysis of all primitively divergent supergraphs ensures, in conjunction with the Slavnov identities, the renormalizability of the theory, once a supersymmetric and gauge invariant regularizing procedure has been introduced. We find that the simplest regularizing procedure is a generalization of the higher covariant derivatives method. In the case of interaction with matter fields we prove that no mass counter term is needed, in exact analogy with the model without gauge fields. Finally we show that, in the Abelian situation, a supersymmetric mass term for the vector multiplet can be introduced without spoiling the renormalizability, thus providing the supersymmetric extension of massive vector bosons theories.     

Asymptotic behaviour of supersymmetric Yang-Mills theories in the two-loop approximation

A calculation of the renormalisation group function β(g) to O(g⁵) for a supersymmetric Yang-Mills theory is presented. It is found that in no case do both the leading terms in the perturbation expansion of β(g) vanish.     

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.     

Renormalization of supersymmetric Yang-Mills theories with soft 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. Received: 19 December 2001 / Published online: 15 March 2002     

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.     

A lagrangian formulation of the Wess approach to supersymmetric Yang-Mills theories

We obtain a superspace lagrangian density which reproduces the Wess formulation of supersymmetric gauge theories. The present approach, which is a first-order formalism, gives rise to a lagrangian density polynomial in the Yang-Mills and auxiliary superfields and appears to be stable under quantization and renormalization.     

Quartic mass matrix and renormalization constants in supersymmetric Yang-Mills theories

We derive the general formula for the supertrace of the quartic mass matrix in a general supersymmetric gauge theory, with arbitrary representations for the chiral multiplets. This formula clarifies the non-renormalization theorems in presence of gauge interactions and gives “extended renormalization theorems” for N = 2 and N = 4 supersymmetric Yang-Mills theories. In particular we find the known result that g_ren = g_bare for the N = 4 theory and the new result m_ren = m_bare for the N = 2 gauge interactions of massive hypermultiplets. We give arguments to the extent that the latter non-renormalization theorem persists to all orders in perturbation theory.     

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.     

Chiral anomalies and constraints on the gauge group in higher-dimensional supersymmetric Yang-Mills theories

Chiral anomalies for gauge theories in any even dimension are computed and the results applied to supersymmetric theories in D = 6, 8 and 10. For D = 8 there is an anomalous chiral U(1) invariance, just as in D = 4, except for certain special groups. For D = 6 and D = 10 there is no anomalous chiral U(1) symmetry, but the gauge current is anomalous except for certain “anomaly-free” groups. For D = 6 the group is thereby constrained to be one of {SU(2), SU(3), exceptional}, while for D = 10 it is constrained to be one of {SU(n) n ≤ 5, USp(4), E₈}.     

On goldstone fields in supersymmetric theories

Some aspects concerning the spontaneous breakdown of global internal symmetries in N = 1 supersymmetric theories are discussed. They can be relevant in the context of supersymmetric preon models. We emphasize the connection of Goldstone dynamics to the linear model. Several statements about the number of Goldstone fields are made. The structure of non-linear lagrangians is discussed. In addition, we consider questions concerning complementarity.     

The anomaly in the Slavnov identity for N = 1 supersymmetric Yang-Mills theories

We solve the consistency conditions of the BRS symmetry in a general N = 1 sypersymmetric Yang-Mills theory with semi-simple gauge group. As a result we find uniquely the supersymmetric extension of the chiral anomaly. Its coefficient is calculated in one loop and does not, in general, vanish. This corrects our earlier statement on the absence of this anomaly.     

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N=2U(k) SYM on R²×(Fuzzy R²) around the minimum of k-coincident fuzzy spheres.     

The quantum dual string wave functional in Yang-Mills theories

From any solution of the classical Yang-Mills equations, we define a string wave functional based on the Wilson loop integral. Its precise definition is given by replacing the string by a finite set of N points, and taking the limit N → ∞. We show that this functional satisfies the Schrödinger equation of the relativistic dual string to leading order in N. We speculate about the relevance of this object to the quantum problem.     

Yang-Mills string theories

It is shown that the addition of a “colored” Yang-Mills supermultiplet to the locally supersymmetric spinning string Lagrangian does not yield a viable new string model, even though supersymmetry is preserved. However, a Yang-Mills extension of the Veneziano string that yields the color singlet sector of the Bardakçi-Halpern model is constructed.     

Algebroid Yang-Mills theories

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead, they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.     

On classification ofN=2 supersymmetric theories

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.     

Renormalization of N = 1 supersymmetric Yang-Mills theories: (I). The classical theory

We investigate the classical N = 1 supersymmetric Yang-Mills theories and pay special attention to the search for the most general action fulfilling the Slavnov identity used to define the theory. It turns out that the well-known action of Ferrara, Zumino and Salam, Strathdee represents a special case, our general solution being equivalent to it through a redefinition of the gauge-fixing condition.