Strings 99

Thomas Thiemann, Albert Einstein Institute, Golm, Germany

This year's major conference on string theory, STRINGSS99, took place in Potsdam, Germany. The conference site was at the University of Potsdam close to the famous Sanssouci Park and the Neues Palais. The meeting was mainily organized by the Albert-Einstein-Institut, Max-Planck-Instititut für Gravitationsphysik, in particular by Olaf Lechtenfeld (University of Hannover), Jan Louis (University of Halle), Dieter Lüst (Humboldt-University Berlin), K. Miesel (University of Potsdam) and Hermann Nicolai (Albert Einstein Institut (AEI)). It was the second meeting of this kind in Europe after Amsterdam in 1997 and enjoyed a record participation number of 380 scientists.

From the scientific point of view, the meeting was one of the more quiet ones with no major breakthroughs reported during the conference, in contrast to the previous one at the ITP, Santa Barbara, where the ADS/CFT correspondence was celebrated. The majority of contributions was rather technical in nature reporting about small progress in various directions.

However, from the political point of view the meeting was even more successful than one could have even dreamt. The local (Berlin, Potsdam and Brandenburg), national (Frankfurter Allgemeine Zeitung (FAZ), Süddeutsche Zeitung etc.) and international (Times, New York Times etc.) press reported about the conference during the entire week, local, national and international broadcasting stations interviewed several scientists mostly from the AEI and it made it even to the first national TV company (ARD) of Germany spending ten percent of its entire time to report about the conference. Furthermore there was a press conference between reporters from all national TV companies and Micheal Green, Stephen Hawking, Hermann Nicolai and Edward Witten as well as public lectures given by Bernard Schutz, Stephen Hawking and Edward Witten explaining their fields of research to public people, students and TV companies. The amount of people that wanted to listen was twice as large as the number of seats. The public interest in quantum gravity, especially by young people, was much higher than to be expected by the declining physics student enrollment numbers in Germany. This week, there is a title page photograph of participants and a corresponding report of the conference in the ``Spiegel", a weakly political magazine which is available throughout the world.

The amount of noise and light that this conference created in the national and international press is outstanding. It is hoped that there will be a positive backreaction for at least string theory-, high energy physics- and quantum gravity related physics science throughout at least Europe and Germany in particular. That this happened was no coincidence : The main organizer of the conference, Hermann Nicolai, took action long before the conference started by informing press, broadcasting and TV stations. On the other hand, that they would pick it up with this amount of enthusiasm was still unexpected.

Coming back to science, the main topics of the conference can be subdivided roughly into the following headlines :

i) Departure from Supersymmetry

One of the main drawbacks of string theory is that at present there is only a perturbative description, apart from the existence of D-branes which are conjectured to be fundamental excitations at strong string coupling while they are solitons at low string coupling. These objects were famously used in stringy black hole calculations in order to probe quantum black holes (strong coupling) at low coupling. This works well, however, only for BPS-D-branes, that is, D-branes which break half of the supersymmetry and therefore low coupling calculations in such a setting are protected against perturbative corrections through supersymmetry. In practice, this means that in string theory one can trust entropy calculations only for extremal (Reissner-Nordstrøm) black holes. There is an effort therefore to generalize this rather non-physical restriction.

Sen, Schwarz, Gaberdiel and Horava reported about constructions of stable non-BPS D-branes, that is, D-branes which do not saturate the Bogomol'ny bound. This can be done by considering string theories declining from the usual world sheet actions with Dirichlet boundary conditions but GSO projections different from the usual ones. The result are Type 0 theories which are not supersymmertic but contain stable (lightest) D-brane states and enable one to test string dualities beyond BPS configurations.

Related were considerations by Klebanov, Blumenhagen, Sagnotti and Kachru who considered D-brane anti-D-brrane pairs. By employing the Omega projection and using tachyon condensates one removes the instabilities from the theory.

ii) Brane Worlds

Famously, the low energy effective action of the closed superstring theories in absence of D-branes contain the Einstein Hilbert term in leading order of the string tension. Antoniadis, Bachas, Ibanez, Ovrut and Verlinde repeated the analysis that led to this result in the presence of D-branes and described possible scenarios that might lead to sub-mm corrections to classical general relativity and might solve the problems of coupling constant unification, stability of the proton and others. Verlinde used ``warped compactifications'' in order to explain the smallness of the cosmological constant. His analysis suggests that 4d gravity couples to matter on the D3 branes and that there is a close relationship between the 5d Einstein equations and the 4d renormalization group.

iii) Black Holes

DeWit described that, if one incorporates higher derivative terms into the computation of the black hole entropy from black p-branes and uses Wald's correction, that one can in fact remove the discrepancy between the quantum statistical entropy and the classical one that was found earlier in certain scenarios like type IIA on a Calabi-Yau 3-fold.

Hawking considered the stability of rotating black holes in AdS spacetimes and found that Kerr black holes are stable.

A very interesting talk was given by Horowitz who considered quasinormal modes of evaporating stringy black holes. A mysterious result is that if one plots the imaginary part of the lowest frequency quasinormal mode against the Schwarzschild radius one finds a linear relation with a coefficient that equals up to 0.2 percent of accuracy the critical exponents that Choptuik found for his critical behaviour analysis of classical black holes with the same matter content. An interpretation is currently not available.

Peet proved a no-hair theorem for stringy black holes corresponding to D-p-branes with $p\le 1$.

iv) Renormalization Group Flows

Gubser and Warner argued that a certain one parameter family of diffeomorphisms in the bulk with parameter r supergravity theory on an AdS background corresponds to a renormalization group flow in the Super-Yang-Mills boundary CFT in the AdS/CFT correspondence. Using this one-parameter family of diffeomorphisms they show that for AdS-metrics of the form ds2=dr2+eA(r) dX2 where dX2 is the four-dimensional Minkowski metric one has $A^{\prime\prime}
\le 0$. This suggests that C=1/(A'(r))3 counts the number of degrees of freedom available to the boundary QFT at the energy scale dual to r and that the exppectation value of the energy momentum tensor scales as C (C-theorem).

v) Wilson Loops

Ooguri and Sonnenschein considered the problem to compute the vacuum expectation value of the Wilson loop operator in the boundary quantum field theory of the AdS/CFT correspondence. Ooguri found that if one translates the BPS condition of D-branes in the bulk into the boundary theory then one obtains restrictions on the shapes of the loop. For such a special loop one can actually compute the Wilson loop operator expectation value and finds that it is finite at least for large g2 N where N is the N of the SU(N) gauge group. Sonnenschein found a finite Lüscher term in the Wilson loop expectation value which describes the quantum fluctuations of the string and one might speculate that these fluctuations are therefore finite.

vi) Non-commutative Gauge Theory

With great interest people waited for the talks by Seiberg and Witten who considered open string theory with a constant non-vanishing anti-symmetric tensor field. One finds that in the limit of vanishing string tension and longitudinal components of the target space metric the effective action is described most easily to all orders in $\alpha'$ by a Yang-Mills theory in the given background spacetime where the gauge field components take values in a non-commutative algebra rather than in the complex numbers. This description has many technical advantages, for instance in the description of instanton moduli spaces as described by Nekrasov and Schwarz.

vii) Others

Staudacher computed Matrix model expectation values by Monte Carlo methods indicating that certain integrals seem to be finite although the matrix model potantial has flat directions. Dijkgraaf and Maldacena reviewed topics in the AdS/CFT correspondence. Polchinsky reported about progress in the DLCQ (discrete light cone quantization) of matrix theory and SYM. Hoppe and Yoneya described open problems in the matrix model approach to M-Theory. Douglas, Mayr, Townsend and Karch reviewed various aspects of supersymmetric p-brane actions. Bousso and Gibbons talked about holography indicating that the correpondence between bulk and boundary theories works only in special cases as for example if the background spacetime is AdS. Kallosh and Berkowits tried quantization of superstrings in AdS spaces (using BRST and twistors) and Ramond-Ramond backgrounds respectively. Green and Obers chose instanton matching as their topics and Theisen gave new insights into gravitational and conformal anomalies.

The conference ended in a summary by David Gross who stated that he missed talks that :
$\bullet$ tested the AdS/CFT correspondence beyond $N=\infty$,
$\bullet$ gave a spacetime description of black hole formation and evaporation,
$\bullet$ gave a dual or holographic description of flat space and cosmology and
$\bullet$ gave a non-perturbative and background independent formulation of ?-theory.
He ended the conference with a ``hello again" in Michigan next year and probably the Tata institute, Mumbai in 2001.

Jorge Pullin