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Register a new userOn the r-matrix of M(embrane)-theory
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Authors
Jens Hoppe
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Supersymmetrizable theories, such as M(em)branes and associated matrix-models related to Yang-Mills theory, possess r-matrices
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We present four infinite series of new quantum theories with super-Poincare symmetry in six dimensions, which are not local quantum field theories. They have string like excitations but the string coupling is of order one. Compactifying these theories on $T^5$ we find a Matrix theory description of M theory on $T^5$ and on $T^5/IZ_2$, which is well defined and is manifestly U-duality invariant.
An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and no boundary-condition constants which allows the positions and partial widths of an arbitrary number levels to be easily fixed in an analysis. These alternative parameters can be converted to standard R-matrix parameters by a straightforward matrix diagonalization procedure. In addition it is possible to express the collision matrix directly in terms of the alternative parameters.
The S-matrix for each chiral sector of Liouville theory on a cylinder is computed from the loop expansion of correlation functions of a one-dimensional field theory on a circle with a non-local kinetic energy and an exponential potential. This action is the Legendre transform of the generating function of semiclassical scattering amplitudes. It is derived from the relation between asymptotic in- and out-fields. Its relevance for the quantum scattering process is demonstrated by comparing explicit loop diagrams computed from this action with other methods of computing the S-matrix, which are also developed.
We study a new class of inhomogeneous pp-wave solutions with 8 unbroken supersymmetries in D=11 supergravity. The 9 dimensional transverse space is Euclidean and split into 3 and 6 dimensional subspaces. The solutions have non-constant gauge flux, which are described in terms of an arbitrary holomorphic function of the complexified 6 dimensional space. The supermembrane and matrix theory descriptions are also provided and we identify the relevant supersymmetry transformation rules. The action also arises through a dimensional reduction of N=1, D=4 supersymmetric Yang-Mills theory coupled to 3 gauge adjoint and chiral multiplets, whose interactions are determined by the holomorphic function of the supergravity solution now constituting the superpotential.
We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine generators for the 12-dimensional bordism group of pin manifolds with a w_1-twisted integer lift of w_4; these are the manifolds on which Wick-rotated M-theory exists. The anomaly cancellation comes down to computing a specific eta-invariant and cubic form on these manifolds. Of interest beyond this specific problem are our expositions of: computational techniques for eta-invariants, the algebraic theory of cubic forms, Adams spectral sequence techniques, and anomalies for spinor fields and Rarita-Schwinger fields.
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