Bullettin String

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28/08/2008

The Standard Model of fundamental interactions provides us with a very successfull description of elementary particle physics up to energies around the TeV scale. The scalar sector however has so far escaped direct experimental evidence and there are too many parameters which are not fixed by the underlying principle of local gauge invariance. Moreover Einstein's gravity turns out to give rise to a non-renormalizable theory at the quantum level and cannot be consistently incorporated into the above framework.

In the past twenty years or so most of the attention of the high energy physics community has been devoted to the study of String Theory that allows for the unification of gravity and the other fundamental interactions in an elegant quantum mechanical scheme. Indeed string amplitudes, such as the original one proposed by Veneziano, tend to be rather soft in the UV because of the extended (one-dimensional) nature of the fundamental constituents involved in the processes and the resulting 'delocalization' of the interactions. The price to pay is very high, however. On the one end the few elementary particles of the Standard Model are to be replaced with an infinite tower of string excitations with increasing masses, separated by the string tension. Moreover the very consistency of string theory, i.e. the absence of Weyl anomalies on the two-dimensional worldsheet, fixes the spacetime dimension to be 26 for the bosonic string and the ambient space to be Ricci flat to lowest order. Last but not least, the ground state of the bosonic string is a tachyon that signals the instability of the perturbative vacuum. Luckily, introducing fermionic degrees of freedom as suggested by Neveu, Scharz and Ramond (NSR) and performing a consistent truncation known as GSO (Gliozzi, Scherk and Olive) projection disposes of the last problem and produces spacetime supersymmetric theories in 10 dimensions.

In order to make contact with standard high energy physics one as to get rid of the extra 6 dimensions. The preferred choice are so called Calabi Yau (CY) spaces with SU(3) holonomy that admit Ricci flat metrics and preserve the minimal amount of supersymmetry in 4 dimensions, i.e. N=1 for type I and heterotic strings and N=2 for type II strings. For about a decade heterotic strings have been considered the most promising ones from a phenomenological perspective since they allow for perturbatively stable supersymmetric vacua with chiral asymmetry and a small number of generations, related to the topology of the internal CY manifold. (Un)fortunately CY spaces are characterize by a large number of parameters that determine their size and shape and correspond to massless scalar fields. Such 'moduli' fields are flat directions of the scalar potential that cannot be lifted in perturbation theory but can be so after the inclusion of non-perturbative effects generated by solitonic or rather istantonic excitations. The first instances are penta-branes, extended objects with 5 spatial dimensions that are magnetically charged with respect to the dual of the massless antisymmetric tensor that invariably appears in all superstring theories. Similar objects with p spatial dimensions were introduced by Dai, Leigh and Polchinski in type II theories and were termed D-branes because of the Dirichlet boundary conditions on the string coordinates transverse to their worlvolumes. All p-branes play a crucial role in establishing deep connections among the five known superstring theories and with 11-dimensional supergravity. Thanks to the presence of stable BPS branes, perturbative dualities such as T-duality, that excahnges large and small volumes, and non-perturbative dualities such as S-duality, that exchanges strong and weak coupling, get unified in bigger U-duality groups which are the discrete remnants of the hidden non-compact symmetries of (extended) supergravity theories describing the low energy limit. The existence of a unifying M-theory (were M stands for 'Mother' or 'Mysterious') can be conjectured in such a way that all known (compactified) superstring theories and 11-dimensional supergravity represent some (perturbative or low energy) limits. The dynamics of its fundamental consistuents, probabily supermembranes or more simply M2-banes, proves harder to analyze than the dynamics of fundamental strings due to the absence of a mass gap in the spectrum. Let alone its solitonic excitations known as M5-branes. On the contrary, (generalized) BPS D-branes admit a fullfledged string description in terms of consistent boundary conditions on two-dimensional conformal field theories (CFT) governing the worldsheet dynamics. Starting from Polchinski's observation that D-branes carry RR-charge, the attention has thus slowly shifted onto theories with open and unoriented strings. These in turn can be viewed as descendants of closed oriented strings which are symmetric under the exchange of left-and right-movers, thanks to the original observation of A. Sagnotti and the systematic construction elaborated over the years by the group in "Tor Vergata". For their work in this field A. Sagnotti and myself (M. Bianchi) have been awarded the SIGRAV prize in 1992. Open-closed string duality turns out to be a very powerful tool in restricting string spectra and interactions and allows for interesting chiral models where the original anomaly cancellation mechanics of Green and Schwarz gets generalized. These theories provide a string basis for brane world scenarios were gravity, mediated by closed string exchange, propagates in the 10-dimensional bulk and gets thus 'diluted', while the other interactions, mediated by open string exchange, are constrained to take place on a (set of) D-branes. Two of the great successes of this approach are a microscopic description of black holes and their Bekenstein-Hawking entropy as bound states of branes, as proposed by Strominger and Vafa, and an incarnation of the holographic principle of 't Hooft and Susskind in the so-called AdS/CFT correspondence proposed by Maldacena. For the first time the long sought for string ansatz for strong interactions, that-one should not forget this!-was the main motivation behind Veneziano amplitude and Polyakov worlsheet approach, seemed to be at reach and an enormous amount of effort has been devoted into the study of the holographic correspondence both in the (super)conformal context and in cases where confinement, chiral symmetry breaking and a mass gap emerge at the end-point of RG flows driven by relevant deformations on the boundary and captured by (supersymmetric) domain wall solutions in the bulk. For his work in this field A. Zaffaroni has been awarded the SIGRAV prize in 2000. The very same philosophy has lead to formulate alternative scenarios to compactifications with warped, possibly non compact, geometries with special holonomy supported by internal fluxes. Longstanding problems such as supersymmetry breaking, moduli stabilization, fermion masses, consistent inflation, large extra dimensions and possibly generation of a (small) cosmological constants can nowadays be quantitatively addressed within phenomenologically viable open string models with intersecting or magnetized D-branes that accomodate some (supersymmetric) extension of the Standard Model. Depending on the scale of the string tension, that can be as low as a few TeV, experimental signatures of the infinite tower of string excitations can be revealed even at LHC!

Last year (2004), the main developments in String Theory have been achieved in the following areas:

- AdS string solitons, super spin chains and integrability
- Flux compactifications, special holonomy and large extra dimensions
- Twistor strings and perturbative string amplitudes
- Higher spin gauge theories and tensionless strings in AdS
- D-brane dynamics and String cosmology
- Black hole physics in String theories

The holographic correspondence between string theory in Anti de Sitter (AdS) space with negative cosmological constant and (super)conformal field theories living on their boundaries has passed many tests over the last few years. For the most interesting case, relating the type IIB superstring on the product space of 5-dimensional AdS and a 5-sphere to N=4 supersymmetric Yang-Mills (SYM) theory in four dimensions, previously unknown non-renormalization properties have been discovered as a consequence of extended superconformal symmetry. In particular regimes however it is possible to test the correspondence beyond the supergravity approximation and match 'unprotected' observables on the two sides of the duality. In particular the sector of operators with large R-charge in N=4 SYM has been conjectured to be captured by the Penrose limit of the product geometry that gives rise to a maximally supersymmetric pp-wave. Similarly operators with large spin have been shown to correspond to long folded strings whose dispersion relation qualitative reproduces the logarithmic growth of the anomalous dimension with the spin thanks to the effect of the boundary region on their rotation.
The problem of resolving the operator mixing and extracting anomalous dimensions of unprotected operators can be conveniently rephrased as the problem of diagonalizing a dilation operator. In the large N limit, the dilatation operator can be viewed as the Hamiltonian of a supersymmetric spin chain that turns out to be integrable at one and two-loops and even three-loops in certain sectors at least. The sophisticated techniques of the Algebraic Bethe Ansatz (ABA) allowed for the computation of the spectrum of anomalous dimensions for a large class of operators with large R-charge and spin. Assuming the validity of the scaling proposed by Berenstein, Maldacena and Nastase (BMN) it has been possible to predict anomalous dimensions at three-loops and find an apparent discrepancy with the results obtained on the string theory side for solitons with the same quantum numbers. The origin of the discrepancy may be ascribed to a subtle non commutativity in the order of taking the limits (large N vs large charge or spin). The same techinques may be applied to models with lower superconformal symmetry and to open spin chains that correspond to operators with non-trivial flavour.

Much effort has been devoted into the study of flux compactifications that correspond to warped geometries with special holonomy. In the low energy effective supergravity limit, turning on fluxes may be described as the gauging of some axionic symmetries. This generates an induced (super)potential that can stabilize most if not all the moduli fields. The drawback of analyses of this kind is the limited control on the backreaction on the geometry and the precise warping and of the higher curvature corrections that enter the determination of the string spectrum beyond the supergravity approximation. Luckily, the effects generated by internal magnetic fluxes in type I compactifications or their T-duals, commonly indicated as un-orientifolds, are completely calculable and may stabilize all the moduli except the dilaton in a supersymmetric fashion, possibly with some large extra dimensions. The resulting brane worlds are T-dual to configurations of interesecting branes of different kinds that have been extensively investigated as a very promising class of string models where some (supersymmetric) extension of the standard model can be accomodated. Combining magnetic fluxes with other geometric deformations supersymmetry breaking can be achieved in a controllable way. A very interesting possibility is the string implementation of the Scherk-Schwarz mechanism that corresponds to freely acting orbifolds, whereby fermions and bosons enjoy different boundary conditions and thus acquire different masses. For his work in this field C. Angelantonj has been awarded the SIGRAV prize in 2004. The vacuum redifinition induced by the presence of tadpoles requires a systematic analysis that has been initiated with some success.

String theory has proven to be a very efficient tool in organizing the numerous independent diagrams appearing in perturbative field theory computations. At each order in perturbation theory, amplitudes involving only closed oriented strings receive a single contribution while amplitudes involving open strings receive a limited number of contributions. A special class of string theories, known as twistor strings, are known to reproduce self-dual Yang Mills theories whose maximally helicity violating amplitudes essentially coincide with similar amplitudes in quantum chromodynamics (QCD). This observation has paved the way to the direct and efficient computation of multi-gluon processes relevant for phenomelogical studies. Parallel to the above applicative studies, there has been a renewed interest in reformulating the computation of perturbative superstring amplitudes beyond one loop both in the standard NSR approach and in the manifestly supersymmetric pure spinor approach pioneered by Barkovits that makes use of GS like 'theta' variables and a peculiar set of worldsheet (super)ghosts.

The long standing problem of the formulation of a consistent theory of interacting higher spin fields has found an elegant solution through the work of Vasilev that heavily relies on the choice of (Anti) de Sitter space rather than flat space-time as starting point. The recent effort in putting this algebraic approach into a more geometrical framework has clearly shown the possible connection with the tensionless limit of superstring theory and holography. Along this line of thought it is natural to expect higher spin symmetry enhancement at small AdS radius.
Extrapolating the string spectrum from large to small radius in AdS₅ x S⁵ one gets a precise matching with the spectrum of single trace gauge invariant operators in N=4 SYM, computed resorting to the method of Polya. Turning on interactions leads to anomalous violation of all but a handful of higher spin currents, whose bulk counterpart is an unprecedented 'pantagruelic' Higgs mechanism that deserves to be termed la Grande Bouffe. The identification of the relevant Stueckelberg fields and the precise form of the mechanism of mass generation may offer the possibility of better understanding relations among mass shifts in the bulk or, equivalently, anomalous dimensions on the boundary that may result as a consequence of the broken higher spin symmetry.

Starting from Sen proposal of interpreting D-brane decay in terms of tachyon condensation, non trivial time dependent backgrounds have been thouroughfully under scrutiny. The dynamics of strings and D-branes in the presence of heavier branes such as pentabranes or gravitational pp waves has been used as a fruitful source of insights in this line of investigation. The possibility of embedding some inflationary scenario and a small but positive cosmological constant in string cosmology is the subject of a very active investigation both in the pre big bang scenario and in more sofisticated models that heavily rely in the above mentioned mechanism of D-brane annihilation. A further bonus of string theory is the possibility of consistently including un-orientifold planes with negative tension whose repulsive effects may be responsible for the avoidance of the initial singularity. This same kind of objects prove very helpful in checking the consistency of string propagation in backgrounds with closed timelike curves (CTC), such as Goedel type universes. In some cases the region where CTC's are present can be consistently excised. In other cases quantization of the Newton constant allow for unitary results even in the presence of CTC.

Despite the successful microscopic interpretation of Bekenstein-Hawking formula for the entropy of near BPS black holes, the problem of understanding higher derivative corrections to BPS geometries has remained dormant for some time. The past couple of years have however witnessed the proposal that the relevant partition function of dyonic black holes, based on a hybrid ensemble where magnetic charges are fixed and electric potential are assigned, could be related to the square modulus of the exponential of the analytic prepotential. The latter is to be evaluated for values of the scalar fields at the horizon determined by the attractor mechanism of Ferrara, Gibbons, Kallosh, and Strominger. Corrections to the original naive formula have been put forward that lead to the 'bubbling' of baby universes very much as the multiplicities of the microstates could be ascribed to the bubbling of BPS geometries.