Supersymmetric Yang-Mills theories in D ⩾ 12

We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9+m, 1 +m) where m = 0, 1, 2,… beyond ten dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous work in 10+2 dimensions to arbitrary even dimensions with the above signature. We have overcome the previously observed obstruction beyond 11+3 dimensions, by the aid of projection operators. Both component and superspace formulations are presented. This also suggests the possibility of consistent supergravity theories in any even dimensions beyond 10+1 dimensions.     

New anomaly-free theories beyond superstrings?

Many new anomaly-free configurations are found group-theoretically, assuming that they contain N = 1 supergravity and Yang-Mills matter with a simple group and allowing the existence of many Yang-Mills singlets (shadow matter).     

Are nonrenormalizable gauge theories renormalizable?

We raise the issue whether gauge theories, that are not renormalizable in the usual powercounting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of terms in the bare action. We find that a theory is renormalizable in this sense if the a priori constraints that we impose on the form of the bare action correspond to the cohomology of the BRST-transformations generated by the action. Recent cohomology theorems of Bamich, Brandt, and Henneaux are used to show that conventionally nomenormalizable theories of Yang-Mills fields (such as quantum chromodynamics with heavy quarks integrated out) and/or gravitation are renormalizable in the modern sense.     

Charged particles in ℤ2 gauge theories

In the free charge phase of the ₂ gauge-Higgs model on a lattice charged particles are shown to exist.Supported by DAADHeisenberg fellow     

Workshop III — Cosmology: Observations versus theories

The topics on which there were presentations in this workshop can broadly be divided into the following categories: Observational aspects of large-scale structures in the universities; phase transitions in the early universe; cosmic microwave background radiation; observational cosmology.     

Testing “microscopic” theories of glass-forming liquids

We assess the validity of “microscopic” approaches of glass-forming liquids based on the sole knowledge of the static pair density correlations. To do so, we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while displaying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhaustive, and we have not tested the effect of adding corrections by including, for instance, three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowdown of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by “microscopic” approaches only requiring the static pair density correlations as nontrivial input.     

The θ-structure in string theories: Superstrings

This paper is the continuation of a previous paper in which the θ-structure of bosonic strings was discussed. In this paper it is pointed out that the SUSYs are broken, both in open strings and closed strings by introducing non-zero parameters θ. The conclusion is that the compact subspace of space-time must not be multiply connected unless the positive energy of the ground state is regularized to be zero.     

Cluster-enriched Yang–Baxter equation from SUSY gauge theories

We propose a new generalization of the Yang–Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang–Baxter equations and supersymmetric gauge theories. The \(S^2\) partition function of a certain 2d \({\mathcal {N}}=(2,2)\) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.     

Nonlinear σ-models and torsion in Kaluza-Klein type theories

It is shown that one can obtain the Lagrangians of nonlinear -models for the scalar curvature of multidimensional spaces of Kaluza-Klein type theories with torsion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 27–31, June, 1989.     

Are wave mechanics and matrix mechanics equivalent theories?

The Eckart and Schrödinger proofs of 1926 are often described as having established the equivalence of wave mechanics and matrix mechanics as physical theories. The objective of this paper is to show that these “proofs” establish nothing of the kind. The Eckart-Schrödinger “proofs” have to do only with the formal identity of two different calculi. The question is, do the “proofs” establish the mathematical identity ofC ₁ andC ₂? Two views are possible: (1) Eckart and Schrödinger subsumed wave mechanics (C ₁) and matrix mechanics (C ₂) within a more comprehensive theory — which might be called “the operator calculus” (O). From this alone it does not follow thatC ₁ andC ₂ are formally identical. In general, the identity of two theories can never be established just by the fact that they both follow from the same premise. The other view (2) is thatO is simply a logical transformer which converts any statement ofC ₁ into a corresponding statement ofC ₂ — without adding any theoretical content of its own. That this is so could never beproved by an inductive selection of typical problems within microphysics; yet this is the actual procedure of Eckart and Schrödinger. Strictly speaking, one could consistently doubt thatC ₁ andC ₂ are ultimately identical even after sympathetically entertaining the Eckart-Schrödinger “proofs”. The really convincing argument for the equivalence asphysical theories of wave mechanics and matrix mechanics was provided by Born's statistical interpretation of theψ-function. Because here, in a frankly inductive procedure, Bornforces a physical interpretation onto bothC ₁ andC ₂ which at last makes it a matter of indifference which algorithm one chooses to express his predictions.     

On Batalin–Vilkovisky formalism of non-commutative field theories

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes–Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra–Itzykson–Zuber integral.     

Lax connections in T■-deformed integrable field theories

In this work,we attempt to construct the Lax connections of TT-deformed integrable field theories in two different ways.With reasonable assumptions,we make an ansatz and find the Lax pairs in the TT-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly.This method is straightforward,but it may be difficult to apply for general models.We then make use of a dynamic coordinate transformation to read the Lax connection in the deformed theory from the undeformed one.We find that once the inverse of the transformation is available,the Lax connection can be read easily.We show the construction explicitly for a few classes of scalar models and find consistency with those determined using the first method.     

Periodic solutions of massive φ 4 and Yang-Mills theories

The well-known connection between the SU(2) gauge theory and the massless ⁴ theory is extended to theories with nonzero mass. Elliptic solutions of these massive theories are given. These are of the plane-wave variety, with independent variable u=p·x where p is a constant four-vector. They depend on a free parameter k. Two of the solutions are generalized plane-waves while the third describes fluctuations about the vacuum solution.     

Can one extract source radii from transport theories?

To know the space-time evolution of a heavy-ion reaction is of great interest, especially in cases where the measured spectra do not allow to ascertain the underlying reaction mechanism. In recent times it became popular to believe that the comparison of Hanbury-Brown-Twiss correlation functions obtained from classical or semiclassical transport theories, like Boltzmann-Ühling-Uhlenbeck (BUU), Quantum Molecular Dynamics (QMD), VENUS, RQMD or ARC, with experiments may provide this insight. It is the purpose of this article to show that this conjecture encounters serious problems. The models which are suited to be compared with the experiments at CERN and Brookhaven are not able to predict a correlation function. Any agreement with existing data has to be considered as accidental. The models suited for lower energies can in principle predict correlation functions. The systematic error may be too large to be of use as far as quantitative conclusions are concerned.     

Cosmological scaling solutions in generalised Gauss–Bonnet gravity theories

The conditions for the existence and stability of cosmological power-law scaling solutions are established when the Einstein–Hilbert action is modified by the inclusion of a function of the Gauss–Bonnet curvature invariant. The general form of the action that leads to such solutions is determined for the case where the universe is sourced by a barotropic perfect fluid. It is shown by employing an equivalence between the Gauss–Bonnet action and a scalar–tensor theory of gravity that the cosmological field equations can be written as a plane autonomous system. It is found that stable scaling solutions exist when the parameters of the model take appropriate values.