Alexander Zhiboedov

Harvard University, Cambridge, Massachusetts, United States

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Publications (25)77.8 Total impact

  • Luis F. Alday · Alexander Zhiboedov
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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 Borel-summable 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 two-loop 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.
    No preview · Article · Oct 2015
  • Xián O. Camanho · José D. Edelstein · Alexander Zhiboedov
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    ABSTRACT: We explore four-dimensional (4D) weakly coupled gravity beyond general relativity in an on-shell language, focusing on the graviton three-point vertex. This admits a novel structure which can be attributed to a term cubic in the Riemann tensor. We consider a generalization of the Shapiro time delay experiment that involves polarized gravitons and show that the new vertex leads to causality violation. Fixing the problem demands the inclusion of an infinite tower of massive higher spin states. Perturbative string theory provides an example of this phenomenon, the only known so far. Interestingly enough, the same argument being applied to inflation suggests that stringy signatures may be hidden in the non-Gaussianities of the primordial gravity wave spectrum.
    No preview · Article · Oct 2015 · International Journal of Modern Physics D
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    Juan Maldacena · David Simmons-Duffin · Alexander Zhiboedov
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    ABSTRACT: We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space 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 double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.
    Preview · Article · Sep 2015
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    Luis F. Alday · Alexander Zhiboedov
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    ABSTRACT: We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone 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.
    Preview · Article · Jun 2015
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    Anatoly Dymarsky · Alexander Zhiboedov
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    ABSTRACT: Known examples of unitary relativistic scale but not conformal-invariant 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.
    Full-text · Article · May 2015 · Journal of Physics A Mathematical and Theoretical
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    Sabrina Pasterski · Andrew Strominger · Alexander Zhiboedov
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    ABSTRACT: The conventional gravitational memory effect is a relative displacement in the position of two detectors induced by radiative energy flux. We find a new type of gravitational `spin memory' in which beams on clockwise and counterclockwise orbits acquire a relative delay induced by radiative angular momentum flux. It has recently been shown that the displacement memory formula is a Fourier transform in time of Weinberg's soft graviton theorem. Here we see that the spin memory formula is a Fourier transform in time of the recently-discovered subleading soft graviton theorem.
    Preview · Article · Feb 2015
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    Andrew Strominger · Alexander Zhiboedov
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    ABSTRACT: The transit of a gravitating radiation pulse past arrays of detectors stationed near future null infinity in the vacuum is considered. It is shown that the relative positions and clock times of the detectors before and after the radiation transit differ by a BMS supertranslation. An explicit expression for the supertranslation in terms of moments of the radiation energy flux is given. The relative spatial displacement found for a pair of nearby detectors reproduces the well-known and potentially measurable gravitational memory effect. The displacement memory formula is shown to be equivalent to Weinberg's formula for soft graviton production.
    Preview · Article · Nov 2014 · Journal of High Energy Physics
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    Xian O. Camanho · Jose D. Edelstein · Juan Maldacena · Alexander Zhiboedov
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    ABSTRACT: We consider higher derivative corrections to the graviton three-point 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 three-point 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 Sitter-like solutions, it indicates the existence of massive higher spin particles if the gravity wave non-gaussianity deviates significantly from the one computed in the Einstein theory.
    Preview · Article · Jul 2014 · Journal of High Energy Physics
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    ABSTRACT: We present a new approach to computing energy-energy correlations in gauge theories that exploits their relation to correlation functions and bypasses the use of scattering amplitudes. We illustrate its power by calculating energy-energy correlations in the maximally supersymmetric Yang-Mills theory in the next-to-leading order approximation.
    Full-text · Article · Feb 2014 · Physical Review Letters

  • No preview · Article · Nov 2013
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    ABSTRACT: We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS 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 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent 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 half-BPS operators obtained from the AdS/CFT correspondence.
    Full-text · Article · Sep 2013 · Nuclear Physics B
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    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 non-trivial 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 well-known results on the four-point correlation function of half-BPS 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 four-point correlation functions in N=4 SYM that should be valid at any coupling and away from the planar limit.
    Full-text · Article · Sep 2013 · Nuclear Physics B
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    Alexander Zhiboedov
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    ABSTRACT: Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy tensor. We analyze energy correlators in parity invariant four-dimensional 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 one-point 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 three-point 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.
    Preview · Article · Apr 2013 · Journal of High Energy Physics
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    Zohar Komargodski · Alexander Zhiboedov
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    ABSTRACT: We consider several aspects of unitary higher-dimensional 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 light-cone 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 gauge-gravity 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.
    Preview · Article · Dec 2012 · Journal of High Energy Physics
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    Alexander Zhiboedov
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    ABSTRACT: We find the form of three-point correlation functions of traceless symmetric conserved currents of arbitrary spin in d-dimensional 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.
    Preview · Article · Jun 2012
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    Juan Maldacena · Alexander Zhiboedov
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    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) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons 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 Wilson-Fisher one and the Gross-Neveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.
    Preview · Article · Apr 2012 · Classical and Quantum Gravity
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    Juan Maldacena · Alexander Zhiboedov
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    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 Coleman-Mandula 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.
    Preview · Article · Dec 2011 · Journal of Physics A Mathematical and Theoretical
  • Alexander V. Zhiboedov
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    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 [hep-th]]. 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 [hep-th]] where the Y-system for scattering amplitudes was found. In the paper [J. Maldacena, A. Zhiboedov, JHEP 1011, 104 (2010). arXiv:1009.1139 [hep-th]] 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 [hep-th]] and later developments of the problem.
    No preview · Article · Jul 2011 · Nuclear Physics B - Proceedings Supplements
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    L. V. Bork · D. I. Kazakov · G. S. Vartanov · A. V. Zhiboedov
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    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.
    Preview · Article · Apr 2011 · Proceedings of the Steklov Institute of Mathematics
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    Juan Maldacena · Alexander Zhiboedov
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    ABSTRACT: We compute form factors in planar N=4 Super Yang-Mills 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 Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension.
    Preview · Article · Sep 2010 · Journal of High Energy Physics