Harmonic Superspaces from Superstrings

We derive harmonic superspaces for N=2,3,4 SYM theory in four dimensions from superstring theory. The pure spinors in ten dimensions are dimensionally reduced and yield the harmonic coordinates. Two anticommuting BRST charges implement Grassmann analyticity and harmonic analyticity. The string field theory action produces the action and field equations for N=3 SYM theory in harmonic superspace.Comment: 14 pp. Harvma

No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons

We reanalyse the question whether the quantum Bogomolnyi bound is saturated in the two-dimensional supersymmetric kink and sine-Gordon models. Our starting point is the usual expression for the one-loop correction to the mass of a soliton in terms of sums over zero-point energies. To regulate these sums, most authors put the system in a box with suitable boundary conditions, and impose an ultraviolet cut-off. We distinguish between an energy cut-off and a mode number cut-off, and show that they lead to different results. We claim that only the mode cut-off yields correct results, and only if one considers exactly the same number of bosonic and fermionic modes in the total sum over bound-state and zero-point energies. To substantiate this claim, we show that in the sine-Gordon model only the mode cut-off yields a result for the quantum soliton mass that is consistent with the exact result for the spectrum as obtained by Dashen et al. from quantising the so-called breather solution. In the supersymmetric case, our conclusion is that contrary to previous claims the quantum Bogomolnyi bound is not saturated in any of the two-dimensional models considered.Comment: 23 pages, LATe

BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory

We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.Comment: 27 pages, 2 figures, latex2e, uses epsfi

Consistent boundary conditions for supergravity

We derive the complete orbit of boundary conditions for supergravity models which is closed under the action of all local symmetries of these models, and which eliminates spurious field equations on the boundary. We show that the Gibbons-Hawking boundary conditions break local supersymmetry if one imposes local boundary conditions on all fields. Nonlocal boundary conditions are not ruled out. We extend our analysis to BRST symmetry and to the Hamiltonian formulation of these models.Comment: 37 pages, v2: references added, v3: misprint correcte

Superstrings and WZNW Models

We give a brief review of our approach to the quantization of superstrings. New is a covariant derivation of the measure at tree level and a path integral formula for this measure.Comment: 12 pp, LaTeX, Contribution to the QTS3 Conference Proceeding