Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.Comment: 36 pages, 3 figures. v2: Refs. adde

The Hagedorn temperature in a decoupled sector of AdS/CFT

We match the Hagedorn/deconfinement temperature of planar N=4 super Yang-Mills (SYM) on R x S^3 to the Hagedorn temperature of string theory on AdS_5 x S^5. The match is done in a near-critical region where both gauge theory and string theory are weakly coupled. On the gauge theory side we are taking a decoupling limit found in hep-th/0605234 in which the physics of planar N=4 SYM is given exactly by the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find moreover a general relation between the Hagedorn/deconfinement temperature and the thermodynamics of the Heisenberg spin chain. On the string theory side, we identify the dual limit which is taken of string theory on a maximally symmetric pp-wave background with a flat direction, obtained from a Penrose limit of AdS_5 x S^5. We compute the Hagedorn temperature of the string theory and find agreement with the Hagedorn/deconfinement temperature computed on the gauge theory side. Finally, we discuss a modified decoupling limit in which planar N=4 SYM reduces to the XXX_{1/2} Heisenberg spin chain with an external magnetic field.Comment: 7 pages. Talk presented by MO at the RTN workshop, Napoli, Oct. 9-13, 200

APPROCCIO CONSEQUENZIALE: IDENTIFICAZIONE DI TECNOLOGIE E PROCESSI MARGINALI PER UN SISTEMA DI PRODUZIONE DI IDROGENO DA BIOMASSA

Lo scopo di questo lavoro è quello di analizzare e valutare come le logiche di mercato (inserite in uno studio di LCA consequenziale), che si determinano a seguito dell’introduzione di una nuova tecnologia per la produzione di idrogeno da biomassa, incidano nella valutazione dei potenziali impatti ambientali. Per far ciò sono stati analizzati i dati predisposti da ENEA, essendo stato affidato all’ente nel 2008 dal Ministero dello Sviluppo Economico, il compito di realizzare il “Censimento del potenziale energetico dalle biomasse” e l’implementazione di una piattaforma software interattiva denominata “Atlante delle Biomasse”. E’ stata effettuata inoltre una ricerca congiunta, in particolare con ENEA ma anche con altri enti che si occupano di biomassa in Italia, per avere contezza degli impieghi attuali di questa risorsa. Si sono anche analizzate le logiche di mercato che si manifestano in seguito all’inserimento della nuova tecnologia a valle, nel settore dei trasporti

Thermal DBI action for the D3-brane at weak and strong coupling

We study the effective action for finite-temperature D3-branes with an electromagnetic field at weak and strong coupling. We call this action the thermal DBI action. Comparing at low temperature the leading $T^4$ correction for the thermal DBI action at weak and strong coupling we find that the $3/4$ factor well-known from the AdS/CFT correspondence extends to the case of arbitrary electric and magnetic fields on the D3-brane. We investigate the reason for this by taking the decoupling limit in both the open and the closed string descriptions thus showing that the AdS/CFT correspondence extends to the case of arbitrary constant electric and magnetic fields on the D3-brane.Comment: 30 pages, no figure

On Three-point Functions in the AdS_4/CFT_3 Correspondence

We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.Comment: 24 pages. v2: typos corrected, references added, published versio

Finite-size corrections to the rotating string and the winding state

We compute higher order finite size corrections to the energies of the circular rotating string on AdS_5 x S^5, of its orbifolded generalization on AdS_5 x S^5/Z_M and of the winding state which is obtained as the limit of the orbifolded circular string solution when J -> infinity and J/M^2 is kept fixed. We solve, at the first order in lambda'=lambda/J^2, where lambda is the 't Hooft coupling, the Bethe equations that describe the anomalous dimensions of the corresponding gauge dual operators in an expansion in m/K, where m is the winding number and K is the "magnon number", and to all orders in the angular momentum J. The solution for the circular rotating string and for the winding state can be matched to the energy computed from an effective quantum Landau-Lifshitz model beyond the first order correction in 1/J. For the leading 1/J corrections to the circular rotating string in m^2 and m^4 and for the subleading 1/J^2 corrections to the m^2 term, we find agreement. For the winding state we match the energy completely up to, and including, the order 1/J^2 finite-size corrections. The solution of the Bethe equations corresponding to the spinning closed string is also provided in an expansion in m/K and to all orders in J.Comment: v2: 33 pages, misprints corrected, references added, version accepted for publication in JHE

The Flowing BIon

In this paper we use the effective blackfold description of branes to extend the study of the thermal BIon, a D-brane and parallel anti-D-brane connected by a wormhole with F-string charge in hot flat space, by introducing a radial boost along the brane. The boosted system behaves qualitatively differently from both the extremal and the thermal BIon considered previously. Interestingly, we are able to formulate a first law of thermodynamics for the system as a whole, despite the fact that it is not a stationary blackfold. In particular, the global temperature is given by the rest frame temperature times the gamma factor of special relativity which is the inverse transformation compared to the case of stationary blackfolds. In addition we define two new kinds of thermodynamic conjugate variables, the energy flux $W$ and the integrated velocity on the brane. We find that a phase transition occurs by varying the energy flux $W$. Below a critical value of $W$ the brane separation $\Delta$ changes only slightly with $W$. Instead above the critical value $\Delta$ grows exponentially.Comment: 26 pages, 6 figures. v2: Introduction and conclusion improved, references adde

The four doors of Islam

This paper - written after a visit in 1987 to the Turkish headquarters of the Jerrahiya, one of the Sufic brotherhoods of Islam - wishes to illustrate in a symbolic form one of the main aspects of this spiritual way representing a classical Sufic formulation of the path to God which is doctrinally and methodologically based on the integration of four levels of truth within the single unifying truth of the key formula La ilaha illa Ilah . In view of the subtlelty of the esoteric subject it deals with, the gnostic apprehension, which traditionally is recognised to be an activity outside the reach of the purely discursive mind, the author has preferred to avoid a strictly academic language and analysis, in an attempt to convey some of the richness and complexity of the spiritual meanings in a holistic, rather than analytical way