The Power of M Theory

TL;DR

The paper addresses whether a fundamental 11D M theory can underlie string theory by exploring a duality between type IIB on $R^9 \times S^1$ and M theory on $R^9 \times T^2$, and by identifying M theory on $R^{10} \times S^1$ with type IIA on $R^{10}$. Using heuristic brane-spectrum matching, it derives explicit tension relations among branes across these theories, showing how 0-, 1-, 2-, 3-, 4-, and 5-branes correspond under compactifications and dualities, and how RR/NS-NS charges map under $SL(2,\mathbb{Z})$ duality. Key results include relations such as $(T_1^{(B)} L_B^2)^{-1} = (T_2^{(M)} A_M^{3/2})/(2\pi)^2$, $\beta^2 = A_M^{1/2} T_2^{(M)}/T_1^{(B)}$, $T_3^{(B)} = (T_1^{(B)})^2/(2\pi)$, and $T_2^{(A)} T_4^{(A)} = T_1^{(A)} T_5^{(A)}$, all of which reinforce a non-perturbative M-theory picture. The work argues for the existence of M theory as a unifying framework and outlines future dualities, including M theory on $R^7 \times K3$ with heterotic strings and M on $R^4 \times S^1 \times K$ with IIA on $R^4 \times K$, while acknowledging unresolved issues surrounding higher-dimensional branes such as a potential 9-brane. This approach provides concrete, testable relations linking brane physics across perturbative and non-perturbative regimes, guiding the search for a fundamental theory beyond perturbation theory.

Abstract

A proposed duality between type IIB superstring theory on R^9 X S^1 and a conjectured 11D fundamental theory (``M theory'') on R^9 X T^2 is investigated. Simple heuristic reasoning leads to a consistent picture relating the various p-branes and their tensions in each theory. Identifying the M theory on R^{10} X S^1 with type IIA superstring theory on R^{10}, in a similar fashion, leads to various relations among the p-branes of the IIA theory.