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A. C. Petkou

Publications and source records attributed to A. C. Petkou.

At least 19 recordsLinked to original sources
arXiv2016

$3d$ fermion-boson map with imaginary chemical potential

We study the three-dimensional $U(N)$ Gross-Neveu and CP$^{N-1}$ models in the canonical formalism with fixed $U(1)$ charge. For large-$N$ this is closely related to coupling the models to abelian Chern-Simons in a monopole background. We show that the presence of the imaginary chemical potential for the $U(1)$ charge makes the phase structure of the models remarkably similar. We calculate their respective large-$N$ free energy densities and show that they are mapped into each other in a precise way. Intriguingly, the free energy map involves the Bloch-Wigner function and its generalizations introduced by Zagier. We expect that our results are connected to the recently discussed $3d$ bosonization.

hep-th↗
arXiv2007

Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex

We apply a recently presented BRST procedure to construct the Largangian cubic vertex of higher-spin gauge field triplets interacting with massive free scalars. In flat space, the spin-s triplet propagates the series of irreducible spin-s, s-2,..,0/1 modes which couple independently to corresponding conserved currents constructed from the scalars. The simple covariantization of the flat space result is not enough in AdS, as new interaction vertices appear. We present in detail the cases of spin-2 and spin-3 triplets coupled to scalars. Restricting to a single irreducible spin-s mode we uncover previously obtained results. We also present an alternative derivation of the lower spin results based on the idea that higher-spin gauge fields arise from the gauging of higher derivative symmetries of free matter Lagrangians. Our results can be readily applied to holographic studies of higher-spin gauge theories.

hep-th↗
arXiv2006

Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields

We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the Higher Spin gauge theory and generalize the Higher Spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction. The generators of this new algebra carry indexes which label the three Higher Spin fields involved into the cubic interaction. The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions. This method can in principle be applied for constructing the Higher Spin interaction vertex at any order. Our results are a first step towards the construction of a Lagrangian for interacting Higher Spin gauge fields that can be holographically studied.

hep-th↗
arXiv2004

Holography, Duality and Higher-Spin Theories

I review recent work on the holographic relation between higher-spin theories in Anti-de Sitter spaces and conformal field theories. I present the main results of studies concerning the higher-spin holographic dual of the three-dimensional O(N) vector model. I discuss the special role played by certain double-trace deformations in Conformal Field Theories that have higher-spin holographic duals. Using the canonical formulation I show that duality transformations in a U(1) gauge theory on AdS4 induce boundary double-trace deformations. I argue that a similar effect takes place in the holography of linearized higher-spin theories on AdS4.

hep-th↗
arXiv2004

Exceptional non-renormalization properties and OPE analysis of chiral four-point functions in N=4 SYM_4

We show that certain classes of apparently unprotected operators in N=4 SYM_4 do not receive quantum corrections as a consequence of a partial non-renormalization theorem for the 4-point function of chiral primary operators. We develop techniques yielding the asymptotic expansion of the 4-point function of CPOs up to order O(λ^2) and we perform a detailed OPE analysis. Our results reveal the existence of new non-renormalized operators of approximate dimension 6.

hep-th↗
arXiv2003

Holography of the N=1 Higher-Spin Theory on AdS4

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.

hep-th↗
arXiv2003

Evaluating the AdS dual of the critical O(N) vector model

We argue that the AdS dual of the three dimensional critical O(N) vector model can be evaluated using the Legendre transform that relates the generating functionals of the free UV and the interacting IR fixed points of the boundary theory. As an example, we use our proposal to evaluate the minimal bulk action of the scalar field that it is dual to the spin-zero ``current'' of the O(N) vector model. We find that the cubic bulk self interaction coupling vanishes. We briefly discuss the implications of our results for higher spin theories and comment on the bulk-boundary duality for subleading N.

hep-th↗
arXiv2002

Rotating Strings in Confining AdS/CFT Backgrounds

We study semiclassical rotating strings in AdS/CFT backgrounds that exhibit both confinement and finite-size effects. The energy versus spin dispersion relation for short strings is the expected Regge trajectory behaviour, with the same string tension as is measured by the Wilson loop. Long strings probe the interplay between confinement and finite-size effects. In particular, the dispersion relation for long strings shows a characteristic dependence on the string tension and the finite-size scale.

hep-th↗
arXiv2002

Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA

We study a class of non-protected local composite operators which occur in the R symmetry singlet channel of the OPE of two stress-tensor multiplets in {\cal N}=4 SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an {\cal N}=1 setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N^2 with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states.

hep-th↗
arXiv2002

Orbiting strings in AdS black holes and N=4 SYM at finite temperature

Following Gubser, Klebanov and Polyakov [hep-th/0204051], we study strings in AdS black hole backgrounds. With respect to the pure AdS case, rotating strings are replaced by orbiting strings. We interpret these orbiting strings as CFT states of large spin similar to glueballs propagating through a gluon plasma. The energy and the spin of the orbiting string configurations are associated with the energy and the spin of states in the dual finite temperature N=4 SYM theory. We analyse in particular the limiting cases of short and long strings. Moreover, we perform a thermodynamic study of the angular momentum transfer from the glueball to the plasma by considering string orbits around rotating AdS black holes. We find that standard expectations, such as the complete thermal dissociation of the glueball, are borne out after subtle properties of rotating AdS black holes are taken into account.

hep-th↗
arXiv2002

Boundary multi-trace deformations and OPEs in AdS/CFT correspondence

We argue that multi-trace deformations of the boundary CFT in AdS/CFT correspondence can arise through the OPE of single-trace operators. We work out the example of a scalar field in AdS_5 with cubic self interaction. By an appropriate reparametrization of the boundary data we are able to deform the boundary CFT by a marginal operator that couples to the conformal anomaly. Our method can be used in the analysis of multi-trace deformations in N=4 SYM where the OPEs of various single-trace operators are known.

hep-th↗
arXiv2001

dS/CFT correspondence on a brane

We study branes moving in an AdS Schwarzschild black hole background. When the brane tension exceeds a critical value, the induced metric on the brane is of FRW type and asymptotically de Sitter. We discuss the relevance of such configurations to dS/CFT correspondence. When the black hole mass reaches a critical value that depends on the brane tension, the brane interpolates in the infinite past and future between a dS space and a finite space of zero Hubble constant. This corresponds to a cosmological evolution without a Big Bang or a Big Crunch. Moreover, the central charge of the CFT dual to the dS brane enters the Cardy-Verlinde formula that gives the entropy of the thermal CFT dual to the bulk AdS black hole.

hep-th↗
arXiv2001

Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling

We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr ϕ^{(i}ϕ^{j)}$ in $\N =4$ SYM$_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading $1/N^2$ corrections to the normalization constants of the 2- and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the {\bf 105}, {\bf 84} and {\bf 175} irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the {\bf 20} irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in $d$ dimensions.

hep-th↗
arXiv2001

Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4

We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4. We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions. We demonstrate the splitting of the free-field theory stress tensor and R-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states respectively. The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling. For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.

hep-th↗
arXiv2001

Universality and a generalized C-function in CFTs with AdS Duals

We argue that the thermodynamics of conformal field theories with AdS duals exhibits a remarkable universality. At strong coupling, a Cardy-Verlinde entropy formula holds even when R-charges or bulk supergravity scalars are turned on. In such a setting, the Casimir entropy can be identified with a generalized C-function that changes monotonically with temperature as well as when non-trivial bulk scalar fields are introduced. We generalize the Cardy-Verlinde formula to cases where no subextensive part of the energy is present and further observe that such a formula is valid for the N=4 super Yang-Mills theory in D=4 even at weak coupling. Finally we show that a generalized Cardy-Verlinde formula holds for asymptotically flat black holes in any dimension.

hep-th↗
arXiv2001

Entropy bounds, monotonicity properties and scaling in CFTs

We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of {\cal N}=4 super Yang-Mills theory in D=4 and the (2,0) tensor multiplet in D=6, the ratio is bounded from above. The corresponding bounds are less stringent than the recently proposed Verlinde bound. We show that entropy bounds arise generically in CFTs in connection to monotonicity properties with respect to temperature changes of a generalized C-function. For strongly coupled CFTs with AdS duals, we show that the ratio obeys the Verlinde bound even in the presence of rotation. For such CFTs, we point out an intriguing resemblance in their thermodynamic formulas with the corresponding ones of two-dimensional CFTs. We show that simple scaling forms for the free energy and entropy of CFTs with AdS duals reproduce the thermodynamical properties of (D+1)-dimensional AdS black holes.

hep-th↗
arXiv2000

Aspects of the conformal operator product expansion in AdS/CFT correspondence

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

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