Publications (22)63.83 Total impact
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ABSTRACT: We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borelsummable expansion. We analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical $O(N)$ model. At large $N$ we reproduce the first few terms in the large spin expansion of the known twoloop anomalous dimensions of higher spin currents in the traceless symmetric representation of $O(N)$ and make further predictions. At small $N$ we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents. 
Article: Looking for a bulk point
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ABSTRACT: We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a positionspace Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of doubletrace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.  [Show abstract] [Hide abstract]
ABSTRACT: We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double lightcone limit and solve for the anomalous dimensions of higher spin currents $\gamma_s$ with large spin $s$. The result depends on the symmetries and the spectrum of the unperturbed conformal field theory. We reproduce all known results and make further predictions. In particular we make a prediction for the anomalous dimensions of higher spin currents in the 3d Ising model.  [Show abstract] [Hide abstract]
ABSTRACT: Known examples of unitary relativistic scale but not conformalinvariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is a free theory. Our discussion applies to an arbitrary number of spacetime dimensions and explains triviality of known SFTs in four spacetime dimensions. We comment on examples of unitary SFTs which are not captured by our construction.Journal of Physics A Mathematical and Theoretical 05/2015; 48(41). DOI:10.1088/17518113/48/41/41FT01 · 1.58 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider higher derivative corrections to the graviton threepoint coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond the one present in the Einstein theory. We argue that these are constrained by causality. We devise a thought experiment involving a high energy scattering process which leads to causality violation if the graviton threepoint vertex contains the additional structures. This violation cannot be fixed by adding conventional particles with spins $J \leq 2$. But, it can be fixed by adding an infinite tower of extra massive particles with higher spins, $J > 2$. In AdS theories this implies a constraint on the conformal anomaly coefficients $\left{a  c \over c} \right \lesssim {1 \over \Delta_{gap}^2}$ in terms of $\Delta_{gap}$, the dimension of the lightest single particle operator with spin $J > 2$. For inflation, or de Sitterlike solutions, it indicates the existence of massive higher spin particles if the gravity wave nongaussianity deviates significantly from the one computed in the Einstein theory.  [Show abstract] [Hide abstract]
ABSTRACT: We present a new approach to computing energyenergy correlations in gauge theories that exploits their relation to correlation functions and bypasses the use of scattering amplitudes. We illustrate its power by calculating energyenergy correlations in the maximally supersymmetric YangMills theory in the nexttoleading order approximation.Physical Review Letters 02/2014; 112(7):071601. DOI:10.1103/PhysRevLett.112.071601 · 7.51 Impact Factor 
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ABSTRACT: We study event shapes in N=4 SYM describing the angular distribution of energy and Rcharge in the final states created by the simplest halfBPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stresstensor supermultiplet: the halfBPS operator itself, the Rsymmetry current and the stress tensor. We present master formulas for the allorder event shapes as convolutions of the Mellin amplitude defining the correlation function of the halfBPS operators, with a couplingindependent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of halfBPS operators obtained from the AdS/CFT correspondence.Nuclear Physics B 09/2013; 884(1). DOI:10.1016/j.nuclphysb.2014.04.019 · 3.93 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a nontrivial analytic continuation which, in the framework of CFT, can elegantly be performed in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N=4 SYM, making use of the wellknown results on the fourpoint correlation function of halfBPS scalar operators. We compute the double scalar flow correlation in N=4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N=4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the fourpoint correlation functions in N=4 SYM that should be valid at any coupling and away from the planar limit.Nuclear Physics B 09/2013; 884(1). DOI:10.1016/j.nuclphysb.2014.04.020 · 3.93 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Unitary conformal field theories (CFTs) are believed to have positive (nonnegative) energy correlators. Energy correlators are universal observables in higherdimensional CFTs built out of integrated Wightman functions of the stressenergy tensor. We analyze energy correlators in parity invariant fourdimensional CFTs. The goal is to use the positivity of energy correlators to further constrain unitary CFTs. It is known that the positivity of the simplest onepoint energy correlator implies that 1/3 <= a/c <= 31/18 where a and c are the Weyl anomaly coefficients. We use the positivity of higher point energy correlators to show that CFTs with extremal values of a/c have trivial scattering observables. More precisely, for a/c=1/3 and a/c=31/18 all energy correlators are fixed to be the ones of the free boson and the free vector theory correspondingly. Similarly, we show that the positivity and finiteness of energy correlators together imply that the threepoint function of the stress tensor in a CFT cannot be proportional to the one in the theory of free boson, free fermion or free vector field.Journal of High Energy Physics 04/2013; 2014(4). DOI:10.1007/JHEP04(2014)038 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider several aspects of unitary higherdimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the lightcone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists tau_1, tau_2 appear in the spectrum, there are operators whose twists are arbitrarily close to tau_1+tau_2. We characterize how tau_1+tau_2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gaugegravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.Journal of High Energy Physics 12/2012; 2013(11). DOI:10.1007/JHEP11(2013)140 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We find the form of threepoint correlation functions of traceless symmetric conserved currents of arbitrary spin in ddimensional conformal field theory (CFT). These are fixed up to several constants by conformal symmetry and current conservation conditions. We present generating functionals for all structures in arbitrary d. In even dimensions we present an interpretation for each structure in terms of the corresponding free field. In odd dimensions d>3 an infinite number of structures is found which are not generated by known CFTs.  [Show abstract] [Hide abstract]
ABSTRACT: We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual large N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one gets in the Vasiliev theories. Namely, the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of order 1/N. Using the slightly broken higher spin symmetry we constrain the three point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) ChernSimons gauge field, the other as a N bosons plus the ChernSimons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points we get the critical O(N) models, both the WilsonFisher one and the GrossNeveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Classical and Quantum Gravity 04/2012; 30(10). DOI:10.1088/02649381/30/10/104003 · 3.17 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the constraints imposed by the existence of a single higher spin conserved current on a three dimensional conformal field theory. A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the ColemanMandula theorem to CFT's, which do not have a conventional S matrix. We also briefly discuss the case where the higher spin symmetries are "slightly" broken.Journal of Physics A Mathematical and Theoretical 12/2011; 46(21). DOI:10.1088/17518113/46/21/214011 · 1.58 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The prescription for calculating form factors at strong coupling in the theories with gravity duals was found in [L. F. Alday, J. Maldacena, JHEP 0711, 068 (2007). arXiv:0710.1060 [hepth]]. The use of integrability for similar objects culminated in the paper [L. F. Alday, J. Maldacena, A. Sever, P. Vieira, J. Phys. A A43, 485401 (2010). arXiv:1002.2459 [hepth]] where the Ysystem for scattering amplitudes was found. In the paper [J. Maldacena, A. Zhiboedov, JHEP 1011, 104 (2010). arXiv:1009.1139 [hepth]] authors extended this scenario to the case of form factors in AdS3 kinematics. Some exact solutions were present. Here we briefly review the results of [J. Maldacena, A. Zhiboedov, JHEP 1011, 104 (2010). arXiv:1009.1139 [hepth]] and later developments of the problem.Nuclear Physics B  Proceedings Supplements 07/2011; 216(1):276277. DOI:10.1016/j.nuclphysbps.2011.05.013 · 0.88 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Using the algorithm of constructing the IR finite observables discussed in detail in our earlier papers, we study the construction of such observables in N = 8 supergravity in the first nontrivial order of perturbation theory. In general, contrary to the amplitudes defined in the presence of some IR regulator, such observables do not reveal any “simple” structure.Proceedings of the Steklov Institute of Mathematics 04/2011; 272(1):3946. DOI:10.1134/S0081543811010056 · 0.30 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We compute form factors in planar N=4 Super YangMills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Ysystem. The integral form of the Ysystem has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of YangYang functional. We consider a restricted set of operators which have small conformal dimension.Journal of High Energy Physics 09/2010; 2010(11). DOI:10.1007/JHEP11(2010)104 · 6.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We discuss formulation of Wilson polygon – MHV amplitude duality at the perturbative level in various regularizations. For four gluons it is shown that at one loop one can formulate diagrammatic correspondence interpolating between the dimensional regularization and the offshell one. We suggest new interpretation of all types of box diagrams in terms of the dual simplex in dimensional regularization and describe its degeneration to the Wilson polygon. The interesting nullification phenomena for the lowenergy amplitudes in the Higgsed phase has been found.Nuclear Physics B 08/2010; 835(3835):343363. DOI:10.1016/j.nuclphysb.2010.04.003 · 3.93 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we give all the details of the calculation that we presented in our previous paper ArXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for ${\cal N}=4$ super YangMills theory was considered in the nexttoleading order of perturbation theory. Explicit cancellation of the infrared divergencies in properly defined inclusive crosssections is demonstrated first in a toy model example of "conformal QED" and then in the real ${\cal N}=4$ SYM theory. We give the fulllength details both for the calculation of the real emission and for the diagrams with splitting in initial and final states. The finite parts for some inclusive differential crosssections are presented in an analytical form. In general, contrary to the virtual corrections, they do not reveal any simple structure. An example of the finite part containing just the log functions is presented. The dependence of inclusive crosssection on the external scale related to the definition of asymptotic states is discussed. Comment: 49 pages, LATEX, 6 eps figures; Minor changes, Refs addedPhysical review D: Particles and fields 11/2009; 81(10). DOI:10.1103/PhysRevD.81.105028 · 4.86 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The infrared structure of MHV gluon amplitudes in planar limit for N=4 super Yang–Mills theory is considered in the nexttoleading order of PT. Explicit cancellation of the infrared divergencies in properly defined crosssections is demonstrated. The remaining finite parts for some inclusive differential crosssections in planar limit are calculated analytically. In general, contrary to the virtual corrections, they do not reveal any simple structure.Physics Letters B 08/2009; 681(3681):296303. DOI:10.1016/j.physletb.2009.10.013 · 6.13 Impact Factor
Publication Stats
484  Citations  
63.83  Total Impact Points  
Top Journals
Institutions

20092014

Princeton University
 Department of Physics
Princeton, New Jersey, United States 
University of Minnesota Duluth
Duluth, Minnesota, United States


2011

Moscow State Forest University
Mytishi, Moskovskaya, Russia


20072009

Joint Institute for Nuclear Research
 Bogoliubov Laboratory of Theoretical Physics
Dubno, Moskovskaya, Russia
