Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces

The vector fields of the quantum Lie algebra are described for the quantum groups $GL_q(N), SL_q(N)$ and $SO_q(N)$ as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms $SU_q(N)$ and $SO_q(N,R)$ are discussed in detail.Comment: 16 pages, Latex, no figures, to appear in the Proceedings of the XX International Conference on Group Theory Methods in Physics, Toyonaka, Japan (1994

A Note on the Chiral Anomaly in the AdS/CFT Correspondence and 1/N^2 Correction

According to the AdS/CFT correspondence,the d=4, N=4 SU(N) SYM is dual to the Type IIB string theory compactified on AdS_5xS^5. A mechanism was proposed previously that the chiral anomaly of the gauge theory is accounted for to the leading order in N by the Chern-Simons action in the AdS_5 SUGRA. In this paper, we consider the SUGRA\string action at one loop and determine the quantum corrections to the Chern-Simons action. While gluon loops do not modify the coefficient of the Chern-Simons action, spinor loops shift the coefficient by an integer. We find that for finite N, the quantum corrections from the complete tower of Kaluza-Klein states reproduce exactly the desired shift N^2 ---> N^2- 1 of the Chern-Simons coefficient, suggesting that this coefficient does not receive corrections from the other states of the string theory. We discuss why this is plausible.Comment: 12 pages, LaTex. Please send any comment to [email protected]; v2: one reference added (to appear in Nucl. Phys. B

Instanton String and M-Wave in Multiple M5-Branes System

We consider the non-abelian self-dual two-form theory arXiv:1203.4224 and find new exact solutions. Our solutions are supported by Yang-Mills (anti)instantons in 4-dimensions and describe wave moving in null directions. We argue and provide evidence that these instanton string solutions correspond to M-wave (MW) on the worldvolume of multiple M5-branes. When dimensionally reduced on a circle, the MW/M5 system is reduced to the D0/D4 system with the D0-branes represented by the Yang-Mills instanton of the D4-branes Yang-Mills gauge theory. We show that this picture is precisely reproduced by the dimensional reduction of our instanton string solutions.Comment: 12 pages. LaTe

Dilaton, Screening of the Cosmological Constant and IR-Driven Inflation

It is known that infrared (IR) quantum fluctuations in de Sitter space could break the de Sitter symmetry and generate time dependent observable effects. In this paper, we consider a dilaton-gravity theory. We find that gravitational IR effects lead to a time dependent shift on the vev of the dilaton and results in a screening (temporal) of the cosmological constant/Hubble parameter. In the Einstein frame, the effect is exponentiated and can give rises to a much more notable amount of screening. Taking the dilaton as inflaton, we obtain an inflationary expansion of the slow roll kind. This inflation is driven by the IR quantum effects of de Sitter gravity and does not rely on the use of a slow roll potential. As a result, our model is free from the eta problem which baffles the standard slow roll inflation models.Comment: 41 pages. 4 figures. v3: Comments on the resummation, quantum corrections to the Friedman equation and an issue of gauge dependence added. References added. Version to appear in JHE