Shun'ya Mizoguchi

MORE ON THE SIMILARITY BETWEEN D = 5 SIMPLE SUPERGRAVITY AND M THEORY

Abstract It has been known that D =5 simple supergravity resembles D =11 supergravity in many respects. We present their further resemblances in (1) the duality groups upon dimensional reduction, and (2) the worldsheet structure of the solitonic string of the D =5 supergravity. We show that the D =3, G 2(+2) / SO (4) (bosonic) nonlinear sigma model is obtained by using Freudenthals construction in parallel to the derivation of the D =3, E 8(+8) / SO (16) sigma model from D =11 supergravity. The zero modes of the string solution with unbroken (4,0) supersymmetry consist of three (non-chiral) scalars, four Majorana-Weyl spinors of the same chirality and one chiral scalar, which suggests a duality to a certain six-dimensional chiral string theory. The worldsheet gravitational anomaly indicates a quantum correction to the Bianchi identity for the dualized two-form gauge field in the bulk just like the M5-brane case.

E10 symmetry in one-dimensional supergravity

We consider dimensional reduction of the eleven-dimensional supergravity to less than four dimensions. The three-dimensional E8(+8)/SO(16) nonlinear sigma model is derived by direct dimensional reduction from eleven dimensions. In two dimensions we explicitly check that the Matzner-Misner-type SL(2, R) symmetry, together with the E8, satisfies the generating relations of E9 under the generalized Geroch compatibility (hypersurface-orthogonality) condition. We further show that an extra SL(2,R) symmetry, which is newly present upon reduction to one dimension, extends the symmetry algebra to a real form of E10. The new SL(2,R acts on certain plane wave solutions propagating at the speed of light. To show that this SL(2,R) cannot be expressed in terms of the old E9 but truly enlarges the symmetry, we compactify the final two dimensions on a two-torus and confirm that it changes the conformal structure of this two-torus.

On discrete U-duality in M-theory

We give a complete set of generators for the discrete exceptional U-duality groups of toroidal compactified type II theory and M-theory in d 3. For this, we use the DSZ quantization in d = 4 as originally proposed by Hull and Townsend, and determine the discrete group inducing integer shifts on the charge lattice. It is generated by fundamental unipotents, which are constructed by exponentiating the Chevalley generators of the corresponding Lie algebra. We then extend a method suggested by the above authors and used by Sen for the heterotic string to obtain the discrete U-duality group in d = 3, thereby obtaining a quantized symmetry in d = 3 from a d = 4 quantization condition. This is studied first in a toy model, corresponding to d = 5 simple supergravity, and then applied to M-theory. It turns out that, in the toy model, the resulting U-duality group in d = 3 is strictly smaller than the one generated by the fundamental unipotents corresponding to all Chevalley generators. However, for M-theory, both groups agree. We illustrate the compactification to d = 3 by an embedding of d = 4 particle multiplets into the d = 3 theory.

Modular invariant critical superstrings on four-dimensional Minkowski space times two-dimensional black hole

Extending the seminal work of Bilal and Gervais, we construct a tachyon-free, modular invariant partition function for critical superstrings on four-dimensional Minkowski × two-dimensional black hole. This model may be thought of as an SL(2,)/U(1) version of Gepner models and corresponds to a conifold point on the moduli space of Calabi-Yau compactifications. We directly deal with N = 2, c = 9 unitary superconformal characters. Modular invariance is achieved by requiring the string to have a momentum along an extra noncompact direction, in agreement with the picture of singular CFTs advocated by Witten. The four-dimensional massless spectrum coincides with that of the tensionless strings, supporting the proposal made by Bershadsky et al. concerning a dual description of type-II strings on a conifold in terms of two intersecting NS5-branes. An interesting relation to D = 6, N = 4 gauged supergravity is also discussed.

Penrose limits and Green–Schwarz strings

We discuss the Green–Schwarz action for type IIB strings in general plane-wave backgrounds obtained as Penrose limits from any IIB supergravity solutions with vanishing background fermions. Using the normal-coordinate expansion in superspace, we prove that the light-cone action is necessarily quadratic in the fermionic coordinates. This proof is valid for more general pp-wave backgrounds under certain conditions. We also write down the complete quadratic action for general bosonic on-shell backgrounds in a form in which its geometrical meaning is manifest both in the Einstein and string frames. When the dilaton and 1-form field strength are vanishing, and the other field strengths are constant, our string-frame action reduces, up to conventions, to the one which has been written down using the supercovariant derivative.

Chiral Generations on Intersecting 5-branes in Heterotic String Theory

We show that there exist two 27 and one

Gravitational corrections for supersymmetric gauge theories with flavors via matrix models

\bold{\overline {27}}

Nonlocal charges of T-dual strings

of E6, net one D = 4,