An approach to systematically implement open-closed string duality for free large N gauge theories is summarised. We show how the relevant closed string moduli space emerges from a reorganisation of the Feynman diagrams contributing to free field correlators. We also indicate why the resulting integrand on moduli space has the right features to be that of a string theory on AdS.

We suggest that M-theory could be non-perturbatively equivalent to a local quantum field theory. More precisely, we present a “renormalizable” gauge theory in eleven dimensions, and show that it exhibits various properties expected of quantum M-theory, most notably the holographic principle of ’t Hooft and Susskind. The theory also satisfies Mach’s principle: A macroscopically large space-time ...

1. Algebraic extensions (1) Let F be a finite field with characteristic p. Prove that |F | = p n for some n. (2) Using f (x) = x 2 + x − 1 and g(x) = x 3 − x + 1, construct finite fields containing 4, 8, 9, 27 elements. Write down multiplication tables for the fields with 4 and 9 elements and verify that the multiplicative groups of these fields are cyclic.

The status of string theory is reviewed, and major recent developments-especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks-are discussed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena,...