Abstract
Chiral algebras in the cohomology of the {overline{Q}}_{+} supercharge of two-dimensional mathcal{N}=left(0,2right) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For mathcal{N}=left(0,2right) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the mathcal{N}=left(2,2right) models and consider some examples.
Highlights
Theoretical physics and deserve attention in various dimensions and with various amounts of supersymmetry
We review the statement that the operator product expansions (OPE) of the cohomology classes can be computed using the free theory and argue that the chiral algebra is tree level exact
The two-dimensional theories with (0, 2) supersymmetry are characterized by the existence of two conserved supercharges Q+ and Q+ of positive chirality acting on the Hilbert space of the theory
Summary
The two-dimensional theories with (0, 2) supersymmetry are characterized by the existence of two conserved supercharges Q+ and Q+ of positive (or right-handed) chirality acting on the Hilbert space of the theory. They satisfy: Q2+ = Q2+ = 0, {Q+, Q+} = 2P++,. These operators obviously satisfy the required relation [Q+, Q+] =. The opposite chirality Fermi superfield satisfies D+Λ = −E(Φ) and is given by:. Written as ∂++v above, should be a derivative of a local field In such a case v above is local and U is the local superfield
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