arXiv subjects

George Georgiou

Publications and source records attributed to George Georgiou.

At least 55 records · Page 3Linked to original sources

arXiv2015

Two and three-point correlators of operators dual to folded string solutions at strong coupling

A particular analytic continuation of classical string solutions having a single AdS_5 spin is considered. These solutions describe strings tunnelling from the boundary to the boundary of AdS_5. We use the Legendre transform of the dimensionally regularised action of these solutions to evaluate the 2-point functions of the dual operators, holographically. Subsequently, we evaluate the structure coefficient of correlators involving two operators with spin S and a BPS state, at strong coupling. Our expressions are valid for any value of the AdS spin S/\sqrtλ and can be applied both at the case of long and short strings. For long strings and at leading order, the structure coefficient is independent of the spin S for twist J operators, while it scales as 1/\log^l{\frac{S}{\sqrtλ}} for the case of operators with two equal angular momenta in S^5. For short strings, the structure coefficient is proportional to the energy E of the string. Finally, we comment on the possibility of relating the strong coupling 3-point function coefficient of three large spin twist 2 operators to the action of the 6-gluon scattering amplitude.

hep-th↗

arXiv2015

Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture

The present study illuminates the relation between null cusped Wilson loops and their corresponding amplitudes. We find that, compared to the case with no self-crossing, the one loop expectation value of a self-intersecting Wilson loop develops an additional 1/εsingularity associated to the intersection. Interestingly, the same 1/εpole exists in the finite part of the one loop amplitude, appearing in the BDS conjecture, at the corresponding kinematic limit. At two loops, we explore the behaviour of the remainder function R, encoding the deviation of the amplitude from the BDS conjecture. By analysing the renormalisation group equations for the Wilson loop with a simple self-crossing, we argue that, when approaching the configuration with a self-crossing (u_2 \to 1, u_1\approx u_3), R diverges in the imaginary direction like R ~ i π\log^3(1-u_2). This behaviour can be attributed to the non-trivial analytic continuation needed when passing from the Euclidean to the physical region and suggests that R has a branch cut in the negative u_2 axis when the two other cross ratios are approximately equal (u_1 \approx u_3).

hep-th↗

arXiv2015

Multi-soft theorems in Gauge Theory from MHV Diagrams

In this work we employ the MHV technique to show that scattering amplitudes with any number of consecutive soft particles behave universally in the multi-soft limit in which all particles go soft simultaneously. After identifying the diagrams which give the leading contribution we give the general rules for writing down compact expressions for the multi-soft factor of m gluons, k of which have negative helicity. We explicitly consider the cases where k equals 1 and 2. In N =4 SYM, the multi-soft factors of 2 scalars or 2 fermions forming a singlet of SU(4) R-symmetry, and m-2 positive helicity gluons are derived. The special case of the double-soft limit gives an amplitude whose leading divergence is 1/δ^2 and not 1/δas in the case of 2 scalars or 2 fermions that do not form a singlet under SU(4). The construction based on the analytic supervertices allows us to obtain simple expressions for the triple-soft limit of 1 scalar and 2 positive helicity fermions, as well as for the quadrapole-soft limit of 4 positive helicity fermions, in a singlet configuration.

hep-th↗

arXiv2015

Entanglement Entropy of the Klebanov-Strassler with dynamical flavors

We present a detailed study of the Entanglement Entropy for the confining Klebanov-Strassler background coupled to a large number of dynamical flavors in the Veneziano limit. As we vary the number of the massless flavors the behavior of the entropy strongly depends on the way we fix the integration constant of the warp factor, that is related to the glueball scale. In the case of massive flavors, the mass of the flavor branes introduces another scale in the background and the entropy undergoes two first order phase transitions. The competition between the glueball and the quark scales will lead to a critical point where one of the phase transitions degenerates to a second order one. We have calculated the critical exponents and have found that they are independent of the number of flavors and different from the mean filed theory expectations.

hep-th↗

arXiv2014

Galaxy clusters and structure formation in quintessence versus phantom dark energy universe

The self-gravitating gas in the Newtonian limit is studied in the presence of dark energy with a linear and constant equation of state. Entropy extremization associates to the isothermal Boltzmann distribution an effective density that includes `dark energy particles', which either strengthen or weaken mutual gravitational attraction, in case of quintessence or phantom dark energy, respectively, that satisfy a linear equation of state. Stability is studied for microcanonical (fixed energy) and canonical (fixed temperature) ensembles. Compared to the previously studied cosmological constant case, in the present work it is found that quintessence increases, while phantom dark energy decreases the instability domain under gravitational collapse. Thus, structures are more easily formed in a quintessence rather than in a phantom dominated Universe. Assuming that galaxy clusters are spherical, nearly isothermal and in hydrostatic equilibrium we find that dark energy with a linear and constant equation of state, for fixed radius, mass and temperature, steepens their total density profile. In case of a cosmological constant, this effect accounts for a 1.5% increase in the density contrast, that is the center to edge density ratio of the cluster. We also propose a method to constrain phantom dark energy.

astro-ph.CO↗

arXiv2014

Large-Spin Expansions of GKP Strings

We demonstrate that the large-spin expansion of the energy of Gubser-Klebanov-Polyakov (GKP) strings that rotate in RxS2 and AdS3 can be expressed in terms of Lambert's W-function. We compute the leading, subleading and next-to-subleading series of exponential corrections to the infinite-volume dispersion relation of GKP strings that rotate in RxS2. These strings are dual to certain long operators of N=4 SYM theory and provide their scaling dimensions at strong coupling. We also show that the strings obey a short-long (strings) duality. For the folded GKP strings that spin inside AdS3 and are dual to twist-2 operators, we confirm the known formulas for the leading and next-to-leading coefficients of their anomalous dimensions and derive the corresponding expressions for the next-to-next-to-leading coefficients.

hep-th↗

arXiv2013

Generalised cusp anomalous dimension in beta-deformed super Yang Mills theory

In this work we study the cusp anomalous dimension of the marginally deformed N=4 sYM theory. We find the expression of the cusp anomalous dimension both at the weak and strong coupling limits. On the gravity side we partially map the system of equations to that of undeformed N=4 sYM, by defining in the internal space an effective angle Δθ_{eff} which depends on the deformation parameter. The cusp anomalous dimension then can be read from that of the N=4 sYM theory, by using this effective angle instead of the usual angle of the undeformed 5-sphere. In the weak coupling regime we find no beta dependence up to two loops. Based on these results we conjecture that for any value of lambda, the cusp anomalous dimension is given by the N=4 sYM result using the coupling dependent effective angle. As a consequence of this, we derive a BPS-like condition between the angle of the AdS space and the Δθ_{eff} of the deformed sphere which when satisfied, nullifies the cusp anomalous dimension.

hep-th↗

arXiv2013

Non-Abelian tensor gauge fields and new topological invariants

In this article we shall consider the tensor gauge fields which are possible to embed into the existing framework of generalized YM theory and therefore allows to construct the gauge invariant and metric independent forms in 2n+4 and 2n+2 dimensions. These new forms are analogous to the Pontryagin-Chern-Simons densities in YM gauge theory and to the corresponding series of densities in 2n+3 dimensions constructed recently in arXiv:1205.0027.

hep-th↗

arXiv2013

Gravothermal instability with a cosmological constant in the canonical ensemble

We present here how the gravothermal or Antonov's instability, which was originally formulated in the microcanonical ensemble, is modified in the presence of a cosmological constant and in the canonical ensemble. In contrast to the microcanonical ensemble, there is a minimum, and not maximum, radius for which metastable states exist. In addition this critical radius is decreasing, and not increasing, with increasing cosmological constant. The minimum temperature for which metastable states exist is decreasing with increasing cosmological constant, while above some positive value of the cosmological constant, there appears a second critical temperature. For lower temperatures than the second critical temperature value, metastable states reappear, indicating a typical reentrant phase transition. The two critical temperatures merge when the cosmological density equals one half the mean density of the system.

astro-ph.CO↗

arXiv2013

Gravitational instabilities of isothermal spheres in the presence of a cosmological constant

Gravitational instabilities of isothermal spheres are studied in the presence of a positive or negative cosmological constant, in the Newtonian limit. In gravity, the statistical ensembles are not equivalent. We perform the analysis both in the microcanonical and the canonical ensembles, for which the corresponding instabilities are known as `gravothermal catastrophe' and `isothermal collapse', respectively. In the microcanonical ensemble, no equilibria can be found for radii larger than a critical value, which is increasing with increasing cosmological constant. In contrast, in the canonical ensemble, no equilibria can be found for radii smaller than a critical value, which is decreasing with increasing cosmological constant. For a positive cosmological constant, characteristic reentrant behaviour is observed.

astro-ph.CO↗

arXiv2013

Correlators of massive string states with conserved currents

We calculate correlation functions of the R-current or the stress-energy tensor T_{μν} with two non-protected operators dual to generic massive string states with rotation in S^5, in the context of the AdS/CFT correspondence. Field theory Ward identities make predictions about the all-loop behaviour of these correlators. In particular, they restrict the fusion coefficient to be proportional to the R-charge of the operators or to their dimension, respectively, with certain coefficients of proportionality. We reproduce these predictions, at strong coupling, using string theory. Furthermore, we point out that the recently observed strong coupling factorisation of 4-point correlators is consistent with conformal symmetry and puts constraints on the strong coupling expressions of 4-point correlators involving R-currents or the stress-energy tensor.

hep-th↗

arXiv2012

Gravothermal Catastrophe with a Cosmological Constant

We investigate the effect of a cosmological constant on the gravothermal catastrophe in the Newtonian limit. A negative cosmological constant acts as a thermodynamic `destabilizer'. The Antonov radius gets smaller and the instability occurs, not only for negative but also for positive energy values. A positive cosmological constant acts as a `stabilizer' of the system, which, in this case, exhibits a novel `reentrant behaviour'. In addition to the Antonov radius we find a second critical radius, where an `inverse Antonov transition' occurs; a series of local entropy maxima is restored.

astro-ph.CO↗

arXiv2012

Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order

We report on a systematic perturbative study of three-point functions in planar SU(N) N=4 super Yang-Mills theory at the one-loop level involving scalar field operators up to length five. For this we have computed a sample of 40 structure constants involving primary operators of up to and including length five which are built entirely from scalar fields. A combinatorial dressing technique has been developed to promote tree-level correlators to one-loop level. In addition we have resolved the mixing up to the order (g_YM)^2 level of the operators involved, which amounts to mixings with bi-fermions, with bi-derivative insertions as well as self-mixing contributions in the scalar sector. This work supersedes a preprint by two of the authors from 2010 which had neglected the mixing contributions.

hep-th↗

arXiv2011

SL(2) sector: weak/strong coupling agreement of three-point correlators

We evaluate three-point correlation functions of single trace operators in N=4 SYM at both weak and strong coupling. We focus on the case where two of the operators belong in a SL(2) sub-sector, and are dual to string solutions in a broad class of solutions with large S and J charges, while the third operator is a BPS state. Perfect agreement between the structure constants at weak and strong coupling is found. Finally, comments on this matching, as well as on the space-time structure of the correlators, are given.

hep-th↗

arXiv2011

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.

hep-th↗

arXiv2011

Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities

We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wilson loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.

hep-th↗

arXiv2011

The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector

The dilatation operator of planar N=4 super Yang-Mills in the pure scalar SO(6) sector is derived at the two-loop order. Representation theory allows for eight free coefficients in an ansatz for the corresponding spin-chain hamiltonian acting on three adjacent scalar states. While four out of these follow from the known SU(2|3) sector two-loop dilatation operator, the remaining four coefficients are derived by diagrammatic techniques and a match to the known dimension of a length three primary operator. Finally, comments upon the use of this result for the evaluation of three-point structure functions of scalar operators at the one-loop order are given.

hep-th↗

arXiv2011

Large spin behavior of anomalous dimensions and short-long strings duality

We are considering the semi-classical string soliton solution of Gubser, Klebanov and Polyakov which represents highly excited states on the leading Regge trajectory, with large spin in $AdS_5$. A prescription relates this soliton solution with the corresponding field theory operators with many covariant derivatives, whose anomalous scaling dimension grows logarithmically with the space-time spin. We explicitly derive the dependence of anomalous dimension on spin for all leading and next-to-leading orders at strong coupling. We develop an iteration procedure which, in principle, allows to derive all terms in the large spin expansion of the anomalous scaling dimension of twist two operators. Our string theory results are consistent with the conjectured "reciprocity" relation, which has been verified to hold in perturbation theory up to five loops in N=4 SYM. We also derive a duality relation between long and short strings.

hep-th↗