The Power of M Theory

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.Comment: 13 pages; late

Duality Symmetries of 4D Heterotic Strings

Target space duality (T duality), which interchanges Kaluza--Klein and winding-mode excitations of the compactified heterotic string, is realized as a symmetry of a world-sheet action. Axion-dilaton duality (S duality), a conjectured nonperturbative SL(2,Z) symmetry of the same theory, plays an analogous role for five-branes. We describe a soliton spectrum possessing both duality symmetries and argue that the theory has an infinite number of dual string descriptions.Comment: 16 pages, NSF-ITP-93-6

Superstring Dualities

This talk is divided into two parts. The first part reviews some of the duality relationships between superstring theories. These relationships are interpreted as providing evidence for the existence of a unique underlying fundamental theory. The second part describes my recent work on the SL(2,Z) duality group of the type IIB superstring theory in ten dimensions and its interpretation in terms of a possible theory of supermembranes in eleven dimensions.Comment: 14 pages; latex; an error has been correcte

Classical Symmetries of Some Two-Dimensional Models Coupled to Gravity

This paper is a sequel to one in which we examined the affine symmetry algebras of arbitrary classical principal chiral models and symmetric space models in two dimensions. It examines the extension of those results in the presence of gravity. The main result is that even though the symmetry transformations of the fields depend on the gravitational background, the symmetry algebras of these classical theories are completely unchanged by the presence of arbitrary gravitational backgrounds. On the other hand, we are unable to generalize the Virasoro symmetries of the flat-space theories to theories with gravity.Comment: 22 pages, late

Interacting Chiral Gauge Fields in Six Dimensions and Born-Infeld Theory

Dimensional reduction of a self-dual tensor gauge field in 6d gives an Abelian vector gauge field in 5d. We derive the conditions under which an interacting 5d theory of an Abelian vector gauge field is the dimensional reduction of a 6d Lorentz invariant interacting theory of a self-dual tensor. Then we specialize to the particular 6d theory that gives 5d Born-Infeld theory. The field equation and Lagrangian of this 6d theory are formulated with manifest 5d Lorentz invariance, while the remaining Lorentz symmetries are realized nontrivially. A string soliton with finite tension and self-dual charge is constructed.Comment: 22 pages, latex, no figure

Lectures on Superstring and M Theory Dualities

These lectures begin by reviewing the evidence for S duality of the toroidally compactified heterotic string in 4d that was obtained in the period 1992--94. Next they review recently discovered dualities that relate all five of the 10d superstring theories and a quantum extension of 11d supergravity called M theory. The study of p-branes of various dimensions (some of which are D-branes) plays a central role. The final sections survey supersymmetric string vacua in 6d and some of the dual constructions by which they can be obtained. Special emphasis is given to a class of N=1 models that exhibit ``heterotic-heterotic duality.''Comment: 67 pages, latex, 1 figure; Lectures given at the ICTP Spring School (March 1996) and the TASI Summer School (June 1996), TASI9

Anomaly-Free Supersymmetric Models in Six Dimensions

The conditions for the cancellation of all gauge, gravitational, and mixed anomalies of $N=1$ supersymmetric models in six dimensions are reviewed and illustrated by a number of examples. Of particular interest are models that cannot be realized perturbatively in string theory. An example of this type, which we verify satisfies the anomaly cancellation conditions, is the K3 compactification of the $SO(32)$ theory with small instantons recently proposed by Witten. When the instantons coincide it has gauge group $SO(32) \times Sp(24)$. Two new classes of models, for which non-perturbative string constructions are not yet known, are also presented. They have gauge groups $SO(2n+8)\times Sp(n)$ and $SU(n)\times SU(n)$, where $n$ is an arbitrary positive integer.Comment: 14 pages, latex; A paragraph in section 4 has been replace

Gauge-Invariant and Gauge-Fixed D-Brane Actions

The first part of this paper presents actions for Dirichlet p-branes embedded in a flat 10-dimensional space-time. The fields of the (p+1)-dimensional world-volume theories are the 10d space-time coordinates $X^m$, a pair of Majorana-Weyl spinors $\theta_1$ and $\theta_2$, and a U(1) gauge field $A_{\mu}$. The N = 2A or 2B super-Poincare group in ten dimensions is realized as a global symmetry. In addition, the theories have local symmetries consisting of general coordinate invariance of the world volume, a local fermionic symmetry (called ``kappa''), and U(1) gauge invariance. A detailed proof of the kappa symmetry is given that applies to all cases (p = 0,1, . . ., 9). The second part of the paper presents gauge-fixed versions of these theories. The fields of the 10d (p = 9) gauge-fixed theory are a single Majorana-Weyl spinor $\lambda$ and the U(1) gauge field $A_{\mu}$. This theory, whose action turns out to be surprisingly simple, is a supersymmetric extension of 10d Born-Infeld theory. It has two global supersymmetries: one represents an unbroken symmetry, and the second corresponds to a broken symmetry for which $\lambda$ is the Goldstone fermion. The gauge-fixed supersymmetric D-brane theories with $p<9$ can be obtained from the 10d one by dimensional reduction.Comment: 33 pages, latex, no figures; revised as requested by refere

Wrapping the M Theory Five-Brane on K3

Using a recently constructed M5-brane world-volume action, we demonstrate that wrapping the M5-brane on K3 gives the heterotic string in seven dimensions. To facilitate the comparison, a new version of the world-sheet action for the Narain-compactified heterotic string, with manifest T duality invariance, is formulated.Comment: 14 pages, latex, no figures; an error has been correcte

Anomalies, Dualities, and Topology of D=6 N=1 Superstring Vacua

We consider various aspects of compactifications of the Type I/heterotic $Spin(32)/\Z_2$ theory on K3. One family of such compactifications includes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of the heterotic $E_8\times E_8$ theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory recently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic $E_8\times E_8$ theory on K3 with instanton numbers (12,12). These connections between $Spin(32)/\Z_2$ and $E_8\times E_8$ models can be demonstrated by T duality, and permit a better understanding of non-perturbative gauge fields in the (12,12) model. In the transformation between $Spin(32)/\Z_2$ and $E_8\times E_8$ models, the strong/weak coupling duality of the (12,12) $E_8\times E_8$ model is mapped to T duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism.Comment: 48 page