Research Interests

Worldline Formalism:

The Worldline Formalism (WF) is a first quantized approach to quantum field theory computations. The idea of using quantum mechanical models to study phenomena which are generally analyzed in second quantization, can be traced back to works by Feynman and Schwinger. However, only recently people have started to use the WF for computation of scattering amplitudes: it has also been applied to QED and QCD (perturbative) computation (see a review).
In 1988 it was shown that quantum mechanical models with N local worldline supersymmetries describe the propagation of N/2-spin particles in a four-dimensional target space. My main interest is the study of the propagation of particles coupled to gravity by funtional integral methods (see [1]-[5]). The WF simplifies the computation, even in presence of a background gravity. Furthermore, it allows to obtain the trace anomaly in a quite elegant and simple fashion. I analyzed in some detail the model with N=2-extended worldline supersymmetries ([4],[5]): such a model is quite interesting since it allowed me to study all the antisymmetric tensor fields allowed by a D-dimensional target space. In [4] the massless case and in [5] the massive one have been worked out.
References:
[1] F. Bastianelli, A. Zirotti - Nucl. Phys. B 642 (2002) 372 [arXiv:hep-th/0205182];
[2] F. Bastianelli, O. Corradini, A. Zirotti - Phys. Rev. D 67, 104009 (2003) [arXiv:hep-th/0211134];
[3] F. Bastianelli, O. Corradini, A. Zirotti - JHEP 0401 (2004) 023 [arXiv:hep-th/0312064];
[4] F. Bastianelli, P. Benincasa, S. Giombi - JHEP 0504 (2005) 010 [arXiv:hep-th/0503155];
[5] F. Bastianelli, P. Benincasa, S. Giombi - JHEP 10 (2005) 114 [arXiv:hep-th/0510010].

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Gauge/Gravity Correspondence:

One of the main achievements of string theory is the conjectured correspondence between gauge theories on a flat D-dimensional space-time and string theories on a curved (D+1)-dimensional space-time [1],[2] (See a review). Being a realization of the holographic principle, in principle the correspondence should relate gauge theiories with the quantum gravity theory. Nowadays we don't really understand quantum gravity, and this means that we don't have the final theory describing gravity beyond the Plank scale, we don't even have a theory which can be really thought of as approaching to be considered "the final" theory of quantum gravity. Anyway, notwithstanding the proliferation of theories of quantum gravity, string theory provides the best answer we got until now.
The importance of this conjecture lies in the fact that it allows us to obtain results about gauge theories by computation in the dual string theory. The dream is to understand better QCD in the strongly coupled regime doing computation in string theory. In such a regime, the gauge theory perturbative approach breaks down and the best results have been obtained by lattice simulations. Anyway, lattice simulations don't provide all the answers we need. Thus, we need one more tool. Unfortunately, we don't really have a string theory dual to the real QCD yet. However, this doesn't mean that we can throw the gauge/string correspondence out. In fact, it allows us to study QCD-like or near-QCD theories so that we can understand better some features which also QCD has (e.g.: confinement).
Typically we get most of informations in the strongly coupled regime by using lattice simulation. Since lattice is Euclidean, it allows us analyze only Euclidean properties of gauge theories. In gauge/string correspondence, a prescription to compute Minkowski correlators has been proposed [3]. What does it means? This means that we can know about Minkowskian properties (e.g.: transport coefficients) of gauge theories by performing calculations in string theory (e.g.: [4]-[8] and references therein). This prescription opened a new research direction, consisting in the study of hydrodynamics of strongly coupled gauge theories. In particular, I analyzed the N=2* model [6] and the Sakai-Sugimoto model [8] in the hydrodynamic limit (i.e.: limit of small frequencies and small momenta keeping their ratio constant). The N=2* model is a mass deformation of the N=4 SYM theory. It is interesting since it is possible to perform computation in both gauge theory side and string theory side. It can therefore be used as a further check of the gauge/gravity correspondence. In [6], the speed of sound and, for the first time in a non-conformal theory, the bulk viscosity have been computed (in the limit of high temperature). More precisely, the speed of sound has been computed by two different methods whose results turn out to coincide. This is a nontrivial check. The Sakai-Sugimoto model is interesting since it shows a confined/deconfined phase transition. It turns out that in this model the viscosity bound is saturated [8]. Moreover, the speed of sound and the bulk viscosity have been computed. Two important points need to be pointed out: first, the speed of sound doesn't depend on any other quantity, but it is a "pure" number (this can be justified if we consider the termodynamics relation relating speed of sound, energy and pressure); second, the speed of sound, shear viscosity and bulk viscosity in this model show the same behaviour as in strongly coupled near-conformal gauge theory plasma. Beside giving informations about gauge theories, these hydrodynamics studies provide further checks on gauge/string correspondence and they might hopefully provide checks on the string theory &alpha'-structure. To this end, in [7] the hydrodynamics of N=4 SYM theory has been analyzed up to the leading order. On string theory side this means that the type IIB string theory with the &alpha' leading correction has been considered. The ratio between shear viscosity and entropy density coincides with the result of a previous computation by Buchel and Liu. Furthermore, the speed of sound and the bulk viscosity don't receive &alpha'-corrections, as expected.
References:
[1] J. Maldacena - Adv. Theor. Math. Phys. 2 (1998) 231 [arXiv:hep-th/9711200];
[2] E. Witten - Adv. Theor. Math. Phys. 2 (1998) 253 [arXiv:hep-th/9802150];
[3] D. T. Son, A. O. Starinets - JHEP 0209 (2002) 042 [arXiv:hep-th/0205051];
[4] G. Policastro, D. T. Son, A. O. Starinets - JHEP 0209 (2002) 026 [arXiv:hep-th/0205052];
[5] G. Policastro, D. T. Son, A. O. Starinets - JHEP 0212 (2002) 054 [arXiv:hep-th/0210220];
[6] P. Benincasa, A. Buchel, A. O. Starinets - Nucl. Phys. B 733 (2006) 160 [arXiv:hep-th/0507026];
[7] P. Benincasa, A. Buchel - JHEP 01 (2006) 103 [arXiv:hep-th/0510041];
[8] P. Benincasa, A. Buchel - Phys. Lett. B 640 (2006) 108 [arXiv:hep-th/0605076];
[9] P. Benincasa, A. Buchel, R. Naryshkin - Phys. Lett. B 645 (2007) 309 [arXiv:hep-th/0610145];

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Open/Closed String Duality:

In a U(N) gauge theory with only fields in the adjoint representation of the gauge group, Feynman diagrams for its partition function can be drawn in the so-called double line notation, where each index is represented by an oriented line. It was shown by 't Hooft [1] that, the free energy can be written as a sum over an index g of the product of N to the power of 2-2g times a function of the 't Hooft coupling &lambda (i.e.: N times the gauge theory coupling constant squared). It was noticed that such an expression, for fixed &lambda, looks like the partition function of a closed string theory with string coupling constant 1/N. Looking at the field theory diagrams in the double line notation as open string diagrams, it is reasonable to conjecture that a gauge theory coming from an open string theory can be equivalently described by a weakly coupled closed string theory. Recently [2]-[4], a new direction was open in this field: a prescription was proposed to construct closed string theories starting from free field theories. Gauge theories with only fields in the adjoint representation of the gauge group are considered in the free field limit. As seen before, Feynman graphs in the double line notation for any perturbative gauge invariant correlators can be organized according to their 't Hooft genus. Given the diagrams for gauge invariant correlators, the homotopically equivalent contractions between any two pairs of vertices are merged together, giving rise to a so-called skeleton graph. It provides a triangulation of the genus g surface. The correlators are conveniently expressed in Schwinger parametrization: in such representation, the Schwinger times are the lenghts of the edges of the original field theory diagrams. Viewing these diagrams as electric circuits, the merging of the homotopically equivalent edges happens according to the rule for parallel electric resistences so that an effective Schwinger time is associated to each skeleton graph edge. It turns out that the moduli space of the skeleton graphs provides a cell decomposition of the stringy moduli space given by the moduli space of genus g surfaces with n punctures times the positive n-dimensional Euclidean space. Moreover, a precise dictionary between skeleton graphs and the closed string theory has been proposed [4] by means of the Strebel differentials (the Strebel lenghts are indentified with the inverse of the Schwinger times). Using this prescription, it has been shown that the worldsheet OPE for the closed string theory originates from the space-time OPE.
References:
[1] G. 't Hooft - Nucl. Phys. B 72 461 (1974);
[2] R. Gopakumar - Phys. Rev. D 70 (2004) 025009 - [arXiv:hep-th/0308184];
[3] R. Gopakumar - Phys. Rev. D 70 (2004) 025010 - [arXiv:hep-th/0402063];
[4] R. Gopakumar - Phys. Rev. D 72 (2005) 066008 - [arXiv:hep-th/0504229];
[5] O. Aharony, Z. Komargodski, S. S. Razamat - JHEP 05 (2006) 016 - [arXiv:hep-th/0308184];
[6] J. R. David, R. Gopakumar - JHEP 07 (2007) 063 - [arXiv:hep-th/0308184].

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