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- W2119137708 abstract "This conference has been devoted to what might be called completely integrable string theories. The last year has seen a proliferation of exact solutions of simple string models (more properly: resummation of the perturbation series around simple solutions of the classical string equations of motion). These models all have one and two dimensional target spaces, a fact directly connected to their solubility. Indeed, it is easy to show that all of the matrix chain models can be rewritten in terms of free fermions which in some sense live on a two dimensional target space. The easiest way to demonstrate this is to write the Mehta et. al.[1] formula for the partition function for a matrix chain with general nearest neighbor transfer matrix1$$Z = int {{d^N}} {lambda _F}{d^N}{lambda _I}Delta left( {{lambda _F}} right)Delta left( {{lambda _I}} right){e^{U({lambda _F}) + U({lambda _I})}}prodlimits_{i = 1}^N { } $$(1.1)$${Gamma _K}(lambda ,k) = {e^{cklambda + {V_K}(lambda ) + {V_K}(k)}}$$(1.2)and use a Grassmann integral representation of the Vandermonde determinants: $$Z = int {{d^N}} varphi F{d^N}varphi I{e^{left[ {varphi _F^i{D_{jk}}varphi _I^k} right]}}$$(1.3)" @default.
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- W2119137708 date "1991-01-01" @default.
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- W2119137708 title "Matrix Models, String Field Theory and Topology" @default.
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- W2119137708 doi "https://doi.org/10.1007/978-1-4615-3772-4_14" @default.
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