Symmetry transformations in Batalin-Vilkovisky formalism

This short note is closely related to Sen-Zwiebach paper on gauge transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate some conditions of physical equivalence of solutions to the quantum master equation and use these conditions to give a very transparent analysis of symmetry transformations in BV-approach. We prove that in some sense every quantum observable (i.e. every even function $H$ obeying $\Delta_{\rho}(He^S)=0$) determines a symmetry of the theory with the action functional $S$ satisfying quantum master equation $\Delta_{\rho}e^S=0$ \endComment: 3 page

Superconducting phase transition in the Nambu - Jona-Lasinio model

The Nambu - Bogoliubov - de Gennes method is applied to the problem of superconducting QCD. The effective quark-quark interaction is described within the framework of the Nambu - Jona-Lasinio model. The details of the phase diagram are given as a function of the strength of the quark-quark coupling constant $G^{\prime}$. It is find that there is no superconducting phase transition when one uses the relation between the coupling constants $G^{\prime}$ and $G$ of the Nambu - Jona-Lasinio model which follows from the Fierz transformation. However, for other values of $G^{\prime}$ one can find a rich phase structure containing both the chiral and the superconducting phase transitions.Comment: 7 pages, 3 figure

How effective are directed credit policies in the United States? A literature survey

Schwarz surveys U.S. experience with directed credit as background for a larger study of the Asian experience. Almost half of net credit lent in the United States annually is directly affected by government policies - half of net credit covering budget deficits, and half falling under various federal credit programs. The main difference between U.S. and Asian credit policy is that U.S. credit policy is oriented more toward equity than toward growth. Different sectors are affected differently by U.S. credit policies. Few empirical studies test how U.S. credit policy affects growth - perhaps partly because of the motives behind those policies. Few enpirical studies even test whether the policies edffectively increase credit to the target group. Schwarz outlines a method for testing the effectiveness of credit policy, then examinesexisting empirical work to see how it fits that methodology. The first common empirical technique examines credit allocation in the economy. Schwarz finds that for the largest program, housing credit, the effect of credit program on credit allocation is very small and may be negative when cross-program effects are considered. The second common empirical technique examines individual sectors. Results here are mixed. In agriculture, much of the credit raises the demand for land, providing a gain for landowners rather than increasing production. In education, less than a third of the students who got government credit would not have gone to college without it. So in both cases, the credit has a positive impact but at a sizable cost. Schwarz concludes that despite its huge volume, directed credit in the United States has a limited impact in growth. The credit programs have generally succeeded in increasing credit to the targeted group, but not necessarily in increasing investment by that group.Banks&Banking Reform,Environmental Economics&Policies,Housing Finance,Financial Intermediation,Economic Theory&Research

Generalized Chern-Simons action and maximally supersymmetric gauge theories

We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the cohomology of super Lie algebras proved in the Appendix.Comment: The talk for the workshop String-Math 2012, Bonn. 22 page

Approximating local observables on projected entangled pair states

Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the computational hardness of contracting projected entangled pair states in two and higher dimensional systems is often seen as a significant obstacle when devising higher-dimensional variants of the density-matrix renormalisation group method. In this work, we show that for those projected entangled pair states that are expected to provide good approximations of such ground states of local Hamiltonians, one can compute local expectation values in quasi-polynomial time. We therefore provide a complexity-theoretic justification of why state-of-the-art numerical tools work so well in practice. We comment on how the transfer operators of such projected entangled pair states have a gap and discuss notions of local topological quantum order. We finally turn to the computation of local expectation values on quantum computers, providing a meaningful application for a small-scale quantum computer.Comment: 7 pages, 1 figure, minor changes in v