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Register a new userCohomologies of the Poisson superalgebra on (2,n)-superdimensional spaces
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Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on R^2 are investigated under suitable continuity restrictions on cochains. The zeroth, first, and second cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a nondegenerate constant Poisson superbracket.
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Poisson superalgebras realized on the smooth Grassmann valued functions with compact support in R^n have the central extensions. The deformations of these central extensions are found.
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^2 taking values in a Grassmann algebra with N generating elements are described up to an equivalence transformation for N e 2.
We study chiral anomalies in $mathcal N=(0, 1)$ and $(0, 2)$ two-dimensional minimal sigma models defined on generic homogeneous spaces $G/H$. Such minimal theories contain only (left) chiral fermions and in certain cases are inconsistent because of incurable anomalies. We explicitly calculate the anomalous fermionic effective action and show how to remedy it by adding a series of local counter-terms. In this procedure, we derive a local anomaly matching condition, which is demonstrated to be equivalent to the well-known global topological constraint on $p_1(G/H)$. More importantly, we show that these local counter-terms further modify and constrain curable chiral models, some of which, for example, flow to nontrivial infrared superconformal fixed point. Finally, we also observe an interesting relation between $mathcal N=(0, 1)$ and $(0, 2)$ two-dimensional minimal sigma models and supersymmetric gauge theories. This paper generalizes and extends the results of our previous publication arXiv:1510.04324.
We study the matrix model for N M2-branes wrapping a Lens space L(p,1) = S^3/Z_p. This arises from localization of the partition function of the ABJM theory, and has some novel features compared with the case of a three-sphere, including a sum over flat connections and a potential that depends non-trivially on p. We study the matrix model both numerically and analytically in the large N limit, finding that a certain family of p flat connections give an equal dominant contribution. At large N we find the same eigenvalue distribution for all p, and show that the free energy is simply 1/p times the free energy on a three-sphere, in agreement with gravity dual expectations.
We consider antiPoisson superalgebras realized on the smooth Grassmann-valued functions with compact supports in R^n and with the grading inverse to Grassmanian parity. The lower cohomologies of these superalgebras are found.
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