arXiv subjects

Michio Kaku

Publications and source records attributed to Michio Kaku.

6 recordsLinked to original sources

arXiv1999

Ultra-violet Behavior of Bosonic Quantum Membranes

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $β= 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.

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arXiv1996

A Note on the Stability of Quantum Supermembranes

We re-examine the question of the stability of quantum supermembranes. In the past, the instability of supermembranes was established by using a regulator, i.e. approximating the membrane by SU(N) super Yang-Mills theory and letting $N \rightarrow \infty$. In this paper, we (a) show that the instability persists even if we directly examine the continuum theory (b) give heuristic arguments that even a theory of unstable membranes at the Planck length may still be compatible with experiment (c) resolve a certain puzzling discrepancy between earlier works on the stability of supermembranes. Presented at the 2nd International Sakharov Conference in Moscow, May 1996.

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arXiv1996

How Unstable Are Fundamental Quantum Supermembranes?

String duality requires the presence of solitonic $p$-branes. By contrast, the existence of fundamental supermembranes is problematic, since they are probably unstable. In this paper, we re-examine the quantum stability of fundamental supermembranes in 11 dimensions. Previously, supermembranes were shown to be unstable by approximating them with SU(n) super Yang-Mills fields as $n \rightarrow \infty$. We show that this instability persists even if we quantize the continuum theory from the very beginning. Second, we speculate how a theory of decaying membranes may still be physically relevant. We present some heuristic arguments showing that light membranes may be too short-lived to be detected, while very massive membranes, with longer lifetimes, may have only very weak coupling to the particles we see in nature. Either way, decaying membranes would not be detectable in the lab. (This article is to be published in Frontiers in Quantum Field Theory (World Scientific) dedicated to Keiji Kikkawa's 60th birthday.)

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arXiv1994

Recent Developments in D=2 String Field Theory

In this review article, we review the recent developments in constructing string field theories that have been proposed, all of which correctly reproduce the correlation functions of two-dimensional string theory. These include: (a) free fermion field theory (b) collective string field theory (c) temporal gauge string field theory (d) non-polynomial string field theory. We analyze discrete states, the $w(\infty)$ symmetry, and correlation functions in terms of these different string field theories. We will also comment on the relationship between these various field theories. (To appear in Int. J. of Mod. Phys. Written in LATEX.)

hep-th↗

arXiv1993

Symmetries and String Field Theory in D=2

(This talk was presented at the Third International Wigner Symposium on Group Theory, Oxford, September, 1993.) Matrix models provides us with the most powerful framework in which to analyze D=2 string theory, yet some of its miraculous features, such as discrete states and $w(\infty)$, remain rather obscure, because the string degrees of freedom have been removed. Liouville theory, on the other hand, has all its string degrees of freedom intact, yet is notoriously difficult to solve. In this paper, we present the second quantized formulation of Liouville theory in D=2, where discrete states and $w(\infty)$ have a natural, field theoretic interpretation. We generalize the non-polynomial closed string field theory, first developed by the author and the Kyoto and MIT groups, to the D=2 case. We find that, in second quantized field theory language, the rather mysterious features of matrix models have an intuitively transparent interpretation, similar to standard gauge theory. Latex file.

hep-th↗

arXiv1993

Sub-Critical Closed String Field Theory in D Less Than 26

We construct the second quantized action for sub-critical closed string field theory with zero cosmological constant in dimensions $ 2 \leq D < 26$, generalizing the non-polynomial closed string field theory action proposed by the author and the Kyoto and MIT groups for $D = 26$. The proof of gauge invariance is considerably complicated by the presence of the Liouville field $ϕ$ and the non-polynomial nature of the action. However, we explicitly show that the polyhedral vertex functions obey BRST invariance to all orders. By point splitting methods, we calculate the anomaly contribution due to the Liouville field, and show in detail that it cancels only if $D - 26 + 1 + 3 Q ^ 2 = 0 $, in both the bosonized and unbosonized polyhedral vertex functions. We also show explicitly that the four point function generated by this action reproduces the shifted Shapiro-Virasoro amplitude found from $c=1$ matrix models and Liouville theory in two dimensions. LATEX file.

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