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.     

Non perturbative anomalies in higher dimensions

We study how nonperturbative anomalies can occur in dimensions higher than four and their implications on the consistency of the theory.     

Internal symmetries from field theories in higher dimensions

It is suggested that a dynamical space-time symmetry group of a given non-linear relativistic theory is able to generate an internal symmetry group. It is shown that onlyO(2N-1, 1) andO(2N, 1) groups are admitted as simple dynamical symmetry groups, and they implyU(2 ^N –2) as the largest internal symmetry groups. The boson and fermion content of the considered models is determined and a new dynamical symmetry breaking mechanism, different from the spontaneous one, is introduced.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.The author would like to thank Professor J. Niederle for the kind hospitality extended to him during his stay at Bechyn.     

Reggeization in Yang-Mills theories

We calculate the high energy fermion-fermion scattering amplitude in Yang-Mills field theory through sixth order in the coupling constant, and find that the amplitude Reggeizes. Our result is simpler than and qualitatively different from an earlier published calculation.     

Parity anomalies in gauge theories in 2 + 1 dimensions

It is shown that the introduction of massless fermions in an abelian gauge theory in 2 + 1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry.     

Stability in Yang-Mills theories

At a solution of the Yang-Mills equations onS ⁴, or the Yang-Mills-Higgs equation on ?³, the hessian of the action functional defines a natural second order, elliptic operator. The number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge. The proof of this assertion requires a relative index theorem for Dirac-type operators on ? ⁿ ,n≧3.     

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.     

Global symmetries in four and higher dimensions

Knowing that a four-dimensional theory with gauge group G₀ is unified in theory with gauge group G puts restrictions on what global symmetries are possible in the low-energy world. Here we analyze those restrictions assuming that unification in G occurs inn four dimensions and assuming that unification occurs only in a higher-dimensional theory. There are possibilities for global symmetries which are not possible in the former case, so in principle indirect evidence for higher dimensions might be found by finding peculiar global symmetries in the low-energy world.     

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}.     

Diffraction scattering in Yang-Mills theories

The infrared problem in Yang-Mills theories is studied in order to elucidate aspects of high energy behavior. The integro-differential equation of Cornwall and Tiktopoulos is used to investigate quark-quark scattering in the limit λ → 0 (λ being the gluon regulator mass), s → ∞ with t fixed. The solution displays the infrared factors explicitly. When this formula is expanded in power series and the leading log is extracted one recovers the perturbation theory calculations to sixth order.     

Self duality in super Yang-Mills theories

The self dual condition in superspace is analysed forN=1,2,4 super Yang-Mills theories. A complete solution of all the constraints in terms of a light cone superfieldJ is presented, where the only equation thatJ satisfies is a SUSY generalization of the Yang equation. By reduction of that equation we obtain various two dimensional SUSY models. We introduce the associated linear problem in terms ofJ, whose integrability condition gives us back the super Yang equation and allows us to obtain the Kac-Moody algebra structure of the theory.     

The pressure in lattice Yang-Mills theories

A simple proof is given that the infinite volume limit for the pressure of a lattice Yang-Mills theory exists and is a continuous function of .     

Effective Lagrangians in classical Yang-Mills theories

The formalism of nonlinear electrodynamics is adapted to the Yang-Mills field theory and it is shown that vacuum polarization effects can be described classically through an effective Lagrangian. As an example, an ad hoc Lagrangian is proposed which leads to a simple solution corresponding to a linear plus Coulomb type potential.     

Nontrivial quadratic gauge-fixing in Yang-Mills theories

We study renormalizability of a quadratic gauge-fixing choice involving gauge fields. We show that this can be renormalized simultaneously maintaining the BRS invariance since this respects the underlying global SU(n) invariance. However, this choice, too, induces quartic ghost terms in conformity with our earlier results. Physics Publication No. 81-099