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High Energy Physics - Theory

arXiv:hep-th/0612154 (hep-th)
[Submitted on 15 Dec 2006 (v1), last revised 15 Mar 2007 (this version, v2)]

Title:Exact classical solutions of nonlinear sigma models on supermanifolds

Authors:Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang
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Abstract: We study two-dimensional nonlinear sigma models with target spaces being the complex super Grassmannian manifolds, that is, coset supermanifolds $G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for $0\leq p \leq m$, $0\leq q \leq n$ and $1\leq p+q$. The projective superspace ${\bf CP}^{m-1|n}$ is a special case of $p=1$, $q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm-Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super case published more than twenty years ago by one of the present authors.
Comments: Latex file, 17 pages; V2, typos corrected, this version will appear in Nucl. Phys. B
Subjects: High Energy Physics - Theory (hep-th); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
Report number: YITP-06-64
Cite as: arXiv:hep-th/0612154
  (or arXiv:hep-th/0612154v2 for this version)
  https://doi.org/10.48550/arXiv.hep-th/0612154
Journal reference: Nucl.Phys.B772:371-384,2007
Related DOI: https://doi.org/10.1016/j.nuclphysb.2007.03.013

Submission history

From: Wen-Li Yang [view email]
[v1] Fri, 15 Dec 2006 02:09:17 UTC (14 KB)
[v2] Thu, 15 Mar 2007 23:46:16 UTC (14 KB)
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