We discuss the current conservation laws in sigma models based on a compact Lie groups of the same dimensionality and connected to each other via pseudoduality transformations in two dimensions. We show that pseudoduality transformations induce an infinite number of nonlocal conserved currents on the pseudodual manifold.
We construct a gauged linear sigma-model representation and develop a 1/N-expansion for flag manifold sigma-models previously proposed by the author. Classically there exists a zero-curvature representation for the equations of motion of these models, which leads in particular to the existence of a conserved non-local charge. We show that at the quantum level this charge is no longer conserved and calculate explicitly the anomaly in its conservation law.
New AdS(3) x G/H compactifications of chiral IIB supergravity
给出了D=10，N=2手征超引力的一类新解.复二形式的场强G_{MNR}的非零背景触发AdS_3 x M_7紧化，其中M_7是一个7维紧致流形.当M_7是非对称陪集空间G/H时，我们总能找到一组协变守恒的常数G_{MNR}，从而满足场方程。例如，G的结构常数在G/H方向上的指数是协变守恒张量。在某些对称G/H中，当这些结构常数为零时，仍可能存在保守的3-形式，得到AdS_3 x G/H解.导出了AdS_3 × M_7紧化的超对称性条件，并对AdS_3 × S^3 × T^4和AdS_3 × S^3 × S^3 × S^1的超对称解进行了检验.最后，我们证明了AdS_3 x S^3 x T^4超对称背景可以看作是AdS_3 x S^3 x CP^2形式的单参数解类中的σ = 0极限，参数σ是CP^2的倒数“半径”。当σ不为0时，所有的超对称性都被破坏。
The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index $\mathcal{I}(J)$ for each spin $J$, with the property that $\mathcal{I}(J)$ is a lower bound on the number of quantum conserved currents of spin $J$. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries…
We compute the free energy in the presence of a chemical potential coupled to a conserved charge in the effective SU(N)xSU(N) scalar field theory to third order for asymmetric volumes in general d-dimensions, using dimensional regularization. We also compute the mass gap in a finite box with periodic boundary conditions.
For classical relativistic field theory in Minkowski space-time, the addition of a superpotential term to a conserved current density is trivial in the sense that it does not modify the local conservation law nor change the conserved charge, though it may allow us to obtain a current density with some improved properties. The addition of a total derivative term to a Lagrangian density is also trivial in the sense that it does not modify the equations of motion of the theory. These facts suggest that both operations are related and possibly equivalent to each other for any global symmetry of an…
