The low-lying mass spectrum of the N = 1 SU(2) SUSY Yang-Mills theory with Wilson fermions

We analyze the low energy spectrum of bound states of the N = 1 SU(2) SUSY Yang-Mills Theory (SYM). This work continues the investigation of the non-perturbative properties of SYM by Monte Carlo simulations in the Wilson discretization with dynamical gluinos. The dynamics of the gluinos is included by the Two-Step Multi-Bosonic Algorithm (TSMB) for dynamical fermions. A new set of configurations has been generated on a lattice at and . The analysis also includes sets of configurations previously generated on a smaller ( ) lattice at and 0.1955. Guided by predictions from low energy Lagrangians, we consider spin-1/2, scalar and pseudoscalar particles. The spectrum of SYM is a challenging subject of investigation because of the extremely noisy correlators. In particular, meson-like correlators contain disconnected contributions. The larger time-extension of the lattice allows to observe two-state signals in the effective mass. Finite-volume effects are monitored by comparing results from the two lattice sizes.Received: 14 September 2004, Revised: 29 October 2004, Published online: 21 December 2004     

N=2 super Yang-Mills theory in projective superspace

We constructN=2 Yang-Mills theory in projective superspace by exploiting the analogy to Ward's twistor construction of self-dual Yang-Mills fields.Work supported in part by NSF grant No. PHY 85-07627     

Perturbative prepotential and monodromies in N = 2 heterotic superstring

We discuss the prepotential describing the effective field theory of N = 2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of the fundamental group of the moduli space minus the singular surfaces. For the simplest two-moduli case, this fundamental group turns out to be a certain braid group and we determine the resulting full duality transformations of the prepotential, which are exact in perturbation theory.     

On the low-energy effective action of N = 2 supersymmetric Yang-Mills theory

We investigate the perturbative part of Seiberg's low-energy effective action of N = 2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on U(1)_R anomaly and non-perturbative β-function arguments.     

Spectrum of boundary states in N=1 SUSY sine-Gordon theory

We consider N=1 supersymmetric sine-Gordon theory (SSG) with supersymmetric integrable boundary conditions (boundary SSG=BSSG). We find two possible ways to close the boundary bootstrap for this model, corresponding to two different choices for the boundary supercharge. We argue that these two bootstrap solutions should correspond to the two integrable Lagrangian boundary theories considered recently by Nepomechie.     

On quasi-self-dual fields in N=4 supersymmetric Yang-Mills theory

A general representation for a quasi-self-dual gauge field which is a generalization of the 't Hooft ansatz is obtained in the Euclidean conformally invariant Yang-Mills theory with a sextuplet of real scalar fields-the boson sector of N=4 supersymmetric Yang-Mills theory. The existence of an O(4)-symmetric quasi-self-dual solution in the region g ²>0 is proved. An explicit example of the quasi-self-dual instanton in the region g ²<0 is constructed.     

N=2 topological Yang-Mills theory on compact Kähler surfaces

We study a topological Yang-Mills theory withN=2 fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact Kähler surfaces. We also study an analogous theory on compact oriented Riemann surfaces and briefly discuss a possible application of Witten's non-Abelian localization formula to the problems in the case of compact Kähler surfaces.This article was typeset by the author using Pjour1     

Higher equations of motion in the N = 1 SUSY Liouville field theory

As in the ordinary bosonic Liouville field theory, in its N = 1 supersymmetric version, an infinite set of operator valued relations, the “higher equations of motions,” hold. The equations are in one to one correspondence with the singular representations of the super Virasoro algebra and enumerated by a pair of natural numbers (m, n). We explicitly demonstrate these equations in the classical case, where the equations of type (1, n) survive and can be interpreted directly as relations for classical fields. The general form of higher equations of motion is established in the quantum case, both for the Neveu-Schwarz and Ramond series. The text was submitted by the authors in English.     

Vanishing three-loop beta function in N = 4 supersymmetric Yang-Mills theory

We have calculated the beta function of the N = 4 supersymmetric Yang-Mills theory through three-loop order and find that it is zero. The calculation was performed using superspace techniques that also allowed the calculation of the complete three-loop chiral-multiplet propagator, which turned out to be quite simple. These results strongly support the speculations that the theory is finite order-by-order in perturbation theory.     

On the renormalization of topological Yang-Mills field theory in N = 1 superspace

We discuss the renormalization aspects of topological super-Yang-Mills field theory in N = 1 superspace. Our approach makes use of the regularization-independent BRS algebraic technique adapted to the case of an N = 1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be a BRS coboundary, implying that the cohomological properties of the supertopological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik β-function of the model by employing a recently discovered supersymmetric antighost Ward identity.     

Wilson loops in $ \mathcal{N} = 2 $ superconformal Yang-Mills theory

We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model.

After constructing interaction terms that impose the boundary conditions, we discuss their implementation at the level of an interacting theory, with a focus on their physical consequences, and the symmetries they preserve. We also derive the effect they have on certain observables, like the Casimir energies.

     

Superconformal field theory and SUSY N=1 KdV hierarchy II: the Q-operator

The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different representations and their truncations are obtained.