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In three spacetime dimensions the worldvolume of a magnetic source is a single point, an event. We make the event dynamical by regarding it as the imprint of a flux-carrying particle impinging from an extra dimension. This can be generalized to higher spacetime dimensions and to extended events. We exhibit universal observable consequences of the existence of events and argue that events are as important as particles or branes. We explain how events arise on the worldvolume of membranes in M theory, and in a Josephson junction in superconductivity., Comment: 4 pages, no figures

We study the fusion of conformal interfaces in the c=1 conformal field theory. We uncover an elegant structure reminiscent of that of black holes in supersymmetric theories. The role of the BPS black holes is played by topological interfaces, which (a) minimize the entropy function, (b) fix through an attractor mechanism one or both of the bulk radii, and (c) are (marginally) stable under splitting. One significant difference is that the conserved charges are logarithms of natural numbers, rather than vectors in a charge lattice, as for BPS states. Besides potential applications to condensed-matter physics and number theory, these results point to the existence of large solution-generating algebras in string theory., Comment: 28 pages, 4 figures. Minor clarifications in v2. Sign Mistakes corrected and reference added in v3

I show that reflection positivity implies that the force between any mirror pair of charge-conjugate probes of the quantum vacuum is attractive. This generalizes a recent theorem of Kenneth and Klich to interacting quantum fields, to arbitrary semiclassical bodies, and to quantized probes with non-overlapping wavefunctions. I also prove that the torques on charge-conjugate probes tend always to rotate them into a mirror-symmetric position., Comment: 13 pages, 1 figure, Latex file. Several points clarified and expanded, two references added.

I analyze the asymptotic symmetries of a theory of gravity in a background consisting of two patches of ${\rm AdS}_3$ spacetime glued together along an ${\rm AdS}_2$ brane. These are generated by a single Virasoro algebra, as expected from the conjectured dual description in terms of a scale-invariant interface separating two conformal field theories. Contributed to the proceedings of the Francqui Colloquium 2001: `Strings and Gravity: Tying the Forces Together .', Comment: 11 pages, Latex file. Minor changes and some extra references

We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view., Comment: Latex file, 34 pages, 8 figures, uses JHEP3.cls. Typos corrected and references added

I review some properties of D-branes in the SU(2) and SL(2,R) WZW models. I comment on a potential difficulty for the realization of `warped brane worlds' in string theory. This short note is based on a talk given at the Strings'01 conference in Mumbay., Comment: 11 pages, Latex, 2 eps figures, uses JHEP.cls

We study D-branes of the ${SL(2,\bR)}$ WZW model, and of its discrete orbifolds. Gluing the currents by group automorphisms leads to three types of D-branes: two-dimensional hyperbolic planes ($H_2$), de Sitter branes (dS$_2$), or anti-de-Sitter branes (AdS$_2$). We explain that the dS$_2$ branes are unphysical, because the electric field on their worldvolume is supercritical. By combining ${SL(2,\bR)}$ and SU(2), we exhibit a class of supersymmetric AdS$_2\times S^2$ three-brane worldvolumes, and consider their possible embeddings in the near-horizon region of stringy black holes. We point out the intriguing difference between the induced and the effective geometries of these D-branes, and speculate on its possible significance., Comment: 34 pages, 6 eps figures, latex, uses JHEP.cls. Final version to appear in JHEP. Minor corrections, and references added

We consider the following two problems: classical domain walls in the $N=1^*$ mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS$_5$ correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory., Comment: Latex, 26 pages, 3 figures, uses JHEP.cls; v4: discussion of holographic interpretation of `fuzzy D-string' configurations modified. Minor esthetic changes otherwise

This is a brief review of the present status, of some recent developments and of the open challenges in string/M theory., Comment: Latex file, 11 pages, 6 figures. Plenary talk at the EPS HEP99 Conference, Tampere, Finland

We explain how D-branes on group manifolds are stabilized against shrinking by quantized worldvolume U(1) fluxes. Starting from the Born-Infeld action in the case of the SU(2) group manifold we derive the masses, multiplicities and spectrum of small fluctuations of these branes, and show that they agree exactly with the predictions of conformal field theory, to all orders in the $\alpha^\prime$ expansion. We discuss the generalization to other groups and comment on an apparent paradox: why are the `RR charges' of these branes not quantized?, Comment: 18 pages, LaTeX. v2: clarifying comment added

I review the arguments in favor of/against the traditional hypothesis that the Planck, string and compactification scales are all within a couple of orders of magnitude from each other. I explain how the extreme brane-world scenario, with TeV type I scale and two large (near millimetric) transverse dimensions, creates conditions analogous to those of the energy desert and is thus naturally singled out. I comment on the puzzle of gauge coupling unification in this context., Comment: Talk given at the Strings 99 Conference (Potsdam, July 1999), latex file (9 pages), uses ioplppt.sty

We consider the elastic scattering of two open strings living on two D-branes separated by a distance $r$. We compute the high-energy behavior of the amplitude, to leading order in string coupling, as a function of the scattering angle $\phi$ and of the dimensionless parameter $v= r/(\pi\alpha^\prime\sqrt{s})$ with $\sqrt{s}$ the center-of-mass energy. The result exhibits an interesting phase diagram in the $(v,\phi)$ plane, with a transition at the production threshold for stretched strings at $v=1$. We also discuss some more general features of the open-string semiclassical world-sheets, and use T-duality to give a quantum tunneling interpretation of the exponential suppression at high-energy., Comment: JHEP class, 18 pages, 8 figures

I review the issue of string and compactification scales in the weak-coupling regimes of string theory. I explain how in the Brane World scenario a (effectively) two-dimensional transverse space that is hierarchically larger than the string length may replace the conventional `energy desert' described by renormalizable supersymmetric QFT. I comment on the puzzle of unification in this context., Comment: 13 pages, LateX. Based on talks given at the conferences `22nd Johns Hopkins workshop' (Goteborg, August 1998), `Fundamental interactions: from symmetries to black holes' in honor of Francois Englert (Brussels, March 1999) and `From Planck Scale to Electroweak Scale' (Bad Honnef, April 1999)

We compute threshold effects to gauge couplings in four-dimensional $Z_N$ orientifold models of type I strings with ${\cal N}=2$ and ${\cal N}=1$ supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality, Comment: 54 pages, LaTeX, comments and references added, final version to appear in Nucl. Phys. B

We derive the complete $(curvature)^2$ terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the $o(\alpha'^2)$ corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3-brane with trivial normal bundle, considerations of $SL(2,\mathbb{Z})$ invariance lead to a complete sum of D-instanton corrections for both the parity-conserving and the parity-violating parts of the effective action. These corrections are required for the cancellation of the modular anomalies of massless modes, and are consistent with the absence of chiral anomalies in the intersection domain of pairs of D-branes. We also show that the parity-conserving part of the non-perturbative R^2 action follows from a one-loop quantum calculation in the six-dimensional world-volume of the M5-brane compactified on a two-torus., Comment: tex file, 31 pages, uses harvmac. Some rewriting of section 2, conclusions and appendix B, in particular in what concerns the discussion of seven-branes in the conclusions and the structure of $\alpha'^2$ terms in appendix B. Other minor corrections plus added references

If the fundamental type-I string scale is of the order of few TeV, the problem of the gauge hierarchy is that of understanding why some dimensions transverse to our brane-world are so large. The technical aspect of this problem, as usually formulated, is `why quantum corrections do not modify drastically the masses and other parameters of the Standard Model'. We argue that within type-I perturbation theory, the technical hierarchy problem is solved (a) if all massless tadpoles cancel locally over distances of order the string length in the transverse space, or (b) if the massless fields with uncancelled local tadpoles propagate `effectively' in $d_\perp \ge 2$ large transverse dimensions. These restrictions ensure that loop corrections to the Standard Model parameters decouple from the four-dimensional Planck scale, except when there are uncancelled tadpoles in $d_\perp =2$ in which case the dependence on $M_P$ is logarithmic. This latter case is thus singled out as the only one in which the origin of the hierarchy would not be attributed entirely to `out of this world' bulk physics. The role of the renormalization group equations in summing the leading large logs is replaced by the classical 2d supergravity equations in the transverse space., Comment: 15 pages, TeX file, harvmac, one eps.figure. Small changes and added references. Final version to appear in Physics Letters B

We establish the existence of a static, classically stable string solution in a region of parameters of the generic two-Higgs Standard Model. In an appropriate limit of parameters, the solution reduces to the well-known soliton of the O(3) non-linear sigma model., Comment: Final version to be published in Physical Review Letters

The occupied and unoccupied fermionic BPS quantum states of a type-IIA string stretched between a D6-brane and an orthogonal D2-brane are described in M-theory by two particular holomorphic curves embedded in a Kaluza-Klein monopole. The absence of multiply-occupied fermionic states --- the Pauli exclusion principle --- is manifested in M-theory by the absence of any other holomorphic curves satisfying the necessary boundary conditions. Stable, non-BPS states with multiple strings joining the D6-brane and D2-brane are described M-theoretically by non-holomorphic curves., Comment: harvmac 6 pages. Final version as published in JHEP

I compare the calculations of special $F^4$ and $R^4$ terms in the (toroidally-compactified) heterotic and type-I effective actions. Besides checking duality, this elucidates the quantitative rules of D-brane calculus. I explain in particular (a) why D-branes do not run in loops, and (b) how their instanton contributions arise from orbifold fixed points of their moduli space. The instanton sum has a simple representation as a sum of the elliptic genera of matrix models., Comment: 7 pages, Latex, one figure, uses espcrc2.sty, Talk at STRINGS'97 (Amsterdam, June 16-21) and HEP-97 (Jerusalem, August 19-26). A misprint in an equation was corrected

We study heterotic/type I duality in d=8,9 uncompactified dimensions. We consider the special (``BPS saturated'') F^4 and R^4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be motivated as arising from a D-brane instanton calculation on the type-I side., Comment: latex 23 pages, 3 figures eps included. Final version to appear in Nuclear Physics B

This is a concise foreword to, rather than a review of D-brane physics., Comment: 20 pages, Latex. To appear in Proceedings of the Workshop on Gauge Theories, Applied Supersymmetry and Quantum Gravity (Imperial College, London, July 1996). Two misprints in eqs. (3.24) and (3.25) corrected

We discuss $F_{\mu\nu}^4$ terms in torroidal compactifications of type-I and heterotic SO(32) string theory. We give a simple argument why only short BPS multiplets contribute to these terms at one loop, and verify heterotic-type-I duality to this order., Comment: 10 pages, Latex. A statement about superinvariants was corrected. Minor cosmetic changes were also made. To appear in Proceedings of Trieste Spring School and Workshop, April 1996

We discuss the equivalence between Type I, Type II and Heterotic N=2 superstring theories in four dimensions. We study the effective field theory of Type I models obtained by orientifold reductions of Type IIB compactifications on $K_3\times T^2$. We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N=2 BPS states that originate from D=6 massless string modes. We apply our result to the so-called S-T-U model which admits simultaneous Type II and Heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture., Comment: 25 pages, LaTeX, 3 figures. Major revision of one-loop open string computations in section 5

We report the results of a numerical search for non-topological solitons in the two-Higgs standard model, characterized by the non-trivial winding, $\pi_3(S^3)$, of the relative phase of the two doublets. In a region of (weak-coupling) parameter space we identify a branch of winding solutions, which are lower in energy than the embedded standard sphaleron and deformed (bi)sphalerons. Contrary, however, to what happens in 2d toy models, these solutions remain unstable even for very large Higgs masses., Comment: 11 LaTeX pages including 3 .eps figures

We analyze the one-loop effective gauge-field action in $Z_2$-orbifold compactifications of type-I theory. We show how, for non-abelian group factors, the threshold effects are ultraviolet finite though given entirely by a six-dimensional field theory expression., Comment: 25 pages, latex. Extra references and minor comments

I calculate the semiclassical phase shift ($\delta$), as function of impact parameter ($b$) and velocity ($v$), when one D-brane moves past another. From its low-velocity expansion I show that, for torroidal compactifications, the moduli space of two identical D-branes stays flat to all orders in $\alpha^\prime$. For K3 compactifications, the calculation of the D-brane moduli-space metric can be mapped to a dual gauge-coupling renormalization problem. In the ultrarelativistic regime, the absorptive part of the phase shift grows as if the D-branes were black disks of area $\sim \alpha^\prime ln{1\over 1-v^2}$. The scattering of large fundamental strings shares all the above qualitative features. A side remark concerns the intriguing duality between limiting electric fields and the speed of light., Comment: 11 pages, latex. References and some extra comments added

We argue that moduli in the adjoint representation of the standard- model gauge group are a natural feature of superstring models, and that they can account for the apparent discrepancy between the string and unification scales., Comment: 5 pages, LaTeX file. Minor modifications, final version to appear in Physics Letters B

I discuss the breaking of space-time supersymmetry when magnetic monopole fields are switched on in compact dimensions., Comment: 3 pages, Latex file (first submission corrupted), talk presented at the Maynooth meeting on "Topics in QFT: Modern Methods in Fundamental Physics", May 1995

We present some non-topological static wall solutions in two-Higgs extensions of the standard model. They are classically stable in a large region of parameter space, compatible with perturbative unitarity and with present phenomenological bounds., Comment: 7 pages, latex, 3 figures available upon request

I study the spontaneous breakdown of supersymmetry when higher-dimensional Yang-Mills or the type-I $SO(32)$ string theory are compactified on magnetized tori. Because of the universal gyromagnetic ratio $g=2$, the splittings of all multiplets are given by the product of charge times internal helicity operators. As a result such compactifications have two remarkable and robust features: {\it (a)} they can reconcile {\it chirality} with {\it extended} low-energy supersymmetry in the limit of large tori, and {\it (b)} they can trigger gauge-symmetry breaking, via Nielsen-Olesen instabilities, at a scale tied classically to $m_{SUSY}$. I exhibit a compactification of the $SO(32)$ superstring, in which magnetic fields break spontaneously $N=4$ supersymmetry, produce the standard-model gauge group with three chiral families of quarks and leptons, and trigger electroweak symmetry breaking. I discuss supertrace relations and the ensuing ultraviolet softness. As with other known mechanisms of supersymmetry breaking, the one proposed here faces two open problems: the threat to perturbative calculability in the decompactification limit, and the problem of gravitational stability and in particular of the cosmological constant. I explain, however, why a good classical description of the vacuum may require small tadpoles for the dilaton, moduli and metric., Comment: 20 pages, Latex file

We present some evidence, based on the analysis of lower-dimensional models, for the possible existence of classically-stable winding solitons in the two-higgs electroweak theory., Comment: 4 pages, latex, no figures Talk at the joint US-Polish workshop on "Physics from the Planck scale to the electroweak scale", Warsaw, September 1994.

We establish the existence of static, classically-stable, winding solitons in renormalizable three-dimensional gauge models, with topologically trivial target space and vacuum manifold. They are prototypes for possible analogous particle-like excitations in the higgs sector of the standard electroweak theory., Comment: 9 pages, LaTeX file. One figure available upon request as a .ps file. Preprint CPTh-A323.0794, Crete-94-14

Spin models on quenched random graphs are related to many important optimization problems. We give a new derivation of their mean-field equations that elucidates the role of the natural order parameter in these models., Comment: 9 pages, report CPTH-A264.1093

We analyze quasi-topological solitons winding around a mexican-hat potential in two space-time dimensions. They are prototypes for a large number of physical excitations, including Skyrmions of the Higgs sector of the standard electroweak model, magnetic bubbles in thin ferromagnetic films, and strings in certain non-trivial backgrounds. We present explicit solutions, derive the conditions for classical stability, and show that contrary to the naive expectation these can be satisfied in the weak-coupling limit. In this limit we can calculate the soliton properties reliably, and estimate their lifetime semiclassically. We explain why gauge interactions destabilize these solitons, unless the scalar sector is extended., Comment: 12p. Latex , Ecole Polytechnique preprint A295.02.94 and Crete preprint 94-10

We identify exact gauge-instanton-like solutions to (super)-string theory using the method of dimensional reduction. We find in particular the Polyakov instanton of 3d QED, and a class of generalized Yang-Mills merons. We discuss their marginal deformations, and show that for the $3d$ instanton they correspond to a dissociation of vector- and axial-magnetic charges., Comment: LateX, 15pp., CERN-TH.7100/93, CPTh-A276.11.93 (Minor Errors Corrected)

I discuss the quantum instability of an electric field in a theory of open strings., Comment: 3p. LATEX , Talk at Rome Workshop on Quantum Gravity, String Theory and Grand Unification, Ecole Polytechnique preprint A232.0393 (Previous submission corrupted by mailer)

The production of o(1/g^2) particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy semiclassically, by discussing two closely-related problems: the large-order behaviour of few-point Green functions, and induced excitation in quantum mechanics. Induced tunneling in the latter case is exponentially enhanced for frequencies of the order of the barrier height., Comment: (13 pages), CPTH/C209-1292 (Talk at the Kiev Conference on: Modern Problems in QFT, Strings and Quantum Gravity, June 1992)

We calculate exactly the rate of pair production of open bosonic and supersymmetric strings in a constant electric field. The rate agrees with Schwinger's classic result in the weak-field limit, but diverges when the electric field approaches some critical value of the order of the string tension. (Phyzzx file), Comment: 13 pages, CPTH-A182.0892