A Lattice Formulation of Two Dimensional Topological Field Theory

We propose a non-perturbative criterion to investigate whether supersymmetric lattice gauge theories preserving partial SUSY can have the desired continuum limit or not. Since the target continuum theories of the lattice models are extended supersymmetric gauge theories including the topological field theory (TFT) as a special subsector, the continuum limits of them should reproduce the properties of the TFT. Therefore, whether the property of the TFT can be recovered at the continuum limit becomes a non-perturbative criterion. Then we accept it as a criterion. In this paper, among the topological properties, we investigate the BRST cohomology on the two dimensional ${\mathcal N}=(4,4)$ CKKU lattice model without moduli fixing mass term. We show that the BRST cohomology in the target continuum theory cannot be realized from the BRST cohomology on the lattice. From this result, we obtain the possible implication that the ${\mathcal N} = (4,4)$ CKKU model cannot recover the target continuum theory if the non-perturbative effects are taken into account.Comment: Submitted for the SUSY07 proceedings, 4 pages, LaTeX, no figure, typos corrected, references adde

Note on massless bosonic states in two-dimensional field theories

In a wide class of $G_L\times G_R$ invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents is completely determined by a fermion one-loop diagram. For any non-trivial fermion content, the two-point function possesses a massless pole which corresponds to massless bosonic physical states. As an application, we show that two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theory without a superpotential possesses $U(1)_L\times U(1)_R$ symmetry and contains one massless bosonic state per fixed spatial momentum. The $\mathcal{N}=(4,4)$ supersymmetric pure Yang-Mills theory possesses $SU(2)_L\times SU(2)_R$ symmetry, and there exist at least three massless bosonic states.Comment: 17pages, 4 figures, uses PTPTeX.cls and feynMF, added an appendi

Perturbative Study of the Supersymmetric Lattice Theory from Matrix Model

We study the lattice model for the supersymmetric Yang-Mills theory in two dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal proof for the absence of susy breaking counter terms as well as the stability of the vacuum by an explicit perturbative calculation for the case of U(2) gauge group. Introducing fermion masses and treating the bosonic zero momentum mode nonperturbatively, we avoid the infra-red divergences in the perturbative calculation. As a result, we find that there appear mass counter terms for finite volume which vanish in the infinite volume limit so that the theory needs no fine-tuning. We also find that the supersymmetry plays an important role in stabilizing the lattice space-time by the deconstruction.Comment: 36 pages, 18 figures; typos corrected, some definitions added, appendix including feynman dyagram delete

M-Theory Superalgebra From Multiple Membranes

We investigate space-time supersymmetry of the model of multiple M2-branes proposed by Bagger-Lambert and Gustavsson. When there is a central element in Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in the central element. Together with the original worldvolume supersymmetry transformation, we construct major part of the eleven dimensional space-time super-Poincar\'{e} algebra with central extensions. Implications to transverse five-branes in the matrix model for M-theory are also discussed.Comment: v1 1+17 pages; v2 refs adde

Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter

We present explicit computations and conjectures for $2 \to 2$ scattering matrices in large $N$ {\it $U(N)$} Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.Comment: 66 pages+ 45 pages appendices, 20 figures, Few typos corrected and few references adde