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By Becker K., Becker M., Schwarz J.

String concept is likely one of the most enjoyable and tough parts of contemporary theoretical physics. This booklet courses the reader from the fundamentals of string concept to fresh advancements. It introduces the fundamentals of perturbative string concept, world-sheet supersymmetry, space-time supersymmetry, conformal box conception and the heterotic string, earlier than describing sleek advancements, together with D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, functions to cosmology and particle physics, black holes in string thought and M-theory, and the microscopic foundation of black-hole entropy. It concludes with Matrix idea, the AdS/CFT duality and its generalizations. This e-book is perfect for graduate scholars and researchers in glossy string concept, and should make a good textbook for a one-year path on string idea. It includes over one hundred twenty routines with options, and over 2 hundred homework issues of suggestions on hand on a password safe web site for academics at

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17) and the value of Λp in Eq. 18), one finds that Eq. 16) is equivalent classically to Eq. 6). For the special case of 2 A different value is actually equivalent, if one makes a corresponding rescaling of hαβ . 17). 30 The bosonic string p = 0, this reproduces the result in Eq. 5) if one makes the identifications T0 = m and h00 = −m2 e2 . 3 String sigma-model action: the classical theory In this section we discuss the symmetries of the string sigma-model action in Eq. 14). This is helpful for writing the string action in a gauge in which quantization is particularly simple.

3 String sigma-model action: the classical theory 35 The terms linear in σ cancel from the sum XRµ + XLµ , so that closed-string boundary conditions are indeed satisfied. 45) m=−∞ +∞ ∂+ XLµ = ls m=−∞ where α0µ = α0µ = 1 µ ls p . 46) These expressions are useful later. In order to quantize the theory, let us first introduce the canonical momentum conjugate to X µ . It is given by δS = T X˙ µ . B. B. 48) = η µν δ(σ − σ ). 49) = T −1 η µν δ(σ − σ ). B. B. B. B. B. = 0. 52) 3 The derivation of the commutation relations for the modes uses the Fourier expansion of the Dirac delta function δ(σ − σ ) = 1 π +∞ X n=−∞ e2in(σ−σ ) .

4 Modern developments in superstring theory 13 tion of M-theory, applicable to certain space-time backgrounds, that goes by the name of Matrix theory. Matrix theory gives a dual description of Mtheory in flat 11-dimensional space-time in terms of the quantum mechanics of N × N matrices in the large N limit. When n of the spatial dimensions are compactified on a torus, the dual Matrix theory becomes a quantum field theory in n spatial dimensions (plus time). There is evidence that this conjecture is correct when n is not too large.

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