arXiv subjects
Juan Maldacena
Publications and source records attributed to Juan Maldacena.
Causality Constraints on Corrections to the Graviton Three-Point Coupling
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 $\left|{a - c \over c} \right| \lesssim {1 \over Δ_{gap}^2}$ in terms of $Δ_{gap}$, 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.
Entropy on a null surface for interacting quantum field theories and the Bousso bound
We study the vacuum-subtracted von Neumann entropy of a segment on a null plane. We argue that for interacting quantum field theories in more than two dimensions, this entropy has a simple expression in terms of the expectation value of the null components of the stress tensor on the null interval. More explicitly $ΔS = 2π\int d^{d-2}y \int_0^1 dx^+\, g(x^+)\, \langle T_{++}\rangle$, where $g(x^+)$ is a theory-dependent function. This function is constrained by general properties of quantum relative entropy. These constraints are enough to extend our recent free field proof of the quantum Bousso bound to the interacting case. This unusual expression for the entropy as the expectation value of an operator implies that the entropy is equal to the modular Hamiltonian, $ΔS = \langle ΔK \rangle $, where $K$ is the operator in the right hand side. We explain how this equality is compatible with a non-zero value for $ΔS$. Finally, we also compute explicitly the function $g(x^+)$ for theories that have a gravity dual.
Proof of a Quantum Bousso Bound
We prove the generalized Covariant Entropy Bound, $ΔS\leq (A-A')/4G\hbar$, for light-sheets with initial area $A$ and final area $A'$. The entropy $ΔS$ is defined as a difference of von Neumann entropies of an arbitrary state and the vacuum, with both states restricted to the light-sheet under consideration. The proof applies to free fields, in the limit where gravitational backreaction is small. We do not assume the null energy condition. In regions where it is violated, we find that the bound is protected by the defining property of light-sheets: that their null generators are nowhere expanding.
Exact results for the entanglement entropy and the energy radiated by a quark
We consider a spherical region with a heavy quark in the middle. We compute the extra entanglement entropy due to the presence of a heavy quark both in ${\cal N}=4 $ Super Yang Mills and in the ${\cal N}=6$ Chern-Simons matter theory (ABJM). This is done by relating the computation to the expectation value of a circular Wilson loop and a stress tensor insertion. We also give an exact expression for the Bremsstrahlung function that determines the energy radiated by a quark in the ABJM theory.
Cool horizons for entangled black holes
General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR pair. We suggest that similar bridges might be present for more general entangled states. In the case of entangled black holes one can formulate versions of the AMPS(S) paradoxes and resolve them. This suggests possible resolutions of the firewall paradoxes for more general situations.
Quantum corrections to holographic entanglement entropy
We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.
Generalized gravitational entropy
We consider classical Euclidean gravity solutions with a boundary. The boundary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation. When the circle is contractible in the bulk, we argue that the entropy of this density matrix is given by the area of a minimal surface. This is a generalization of the usual black hole entropy formula to euclidean solutions without a Killing vector. A particular example of this set up appears in the computation of the entanglement entropy of a subregion of a field theory with a gravity dual. In this context, the minimal area prescription was proposed by Ryu and Takayanagi. Our arguments explain their conjecture.
Time Evolution of Entanglement Entropy from Black Hole Interiors
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
The Thermal Free Energy in Large N Chern-Simons-Matter Theories
We compute the thermal free energy in large N U(N) Chern-Simons-matter theories with matter fields (scalars and/or fermions) in the fundamental representation, in the large temperature limit. We note that in these theories the eigenvalue distribution of the holonomy of the gauge field along the thermal circle does not localize even at very high temperatures, and this affects the computation significantly. We verify that our results are consistent with the conjectured dualities between Chern-Simons-matter theories with scalar fields and with fermion fields, as well as with the strong-weak coupling duality of the N=2 supersymmetric Chern-Simons-matter theory.
Entanglement entropy in de Sitter space
We compute the entanglement entropy for some quantum field theories on de Sitter space. We consider a superhorizon size spherical surface that divides the spatial slice into two regions, with the field theory in the standard vacuum state. First, we study a free massive scalar field. Then, we consider a strongly coupled field theory with a gravity dual, computing the entanglement using the gravity solution. In even dimensions, the interesting piece of the entanglement entropy is proportional to the number of e-foldings that elapsed since the spherical region was inside the horizon. In odd dimensions it is contained in a certain finite piece. In both cases the entanglement captures the long range correlations produced by the expansion.
An exact formula for the radiation of a moving quark in N=4 super Yang Mills
We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in N=4 super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
We derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on a Wilson loop with charge L. In the large L limit the problem can be solved in terms of a certain boundary reflection matrix. We determine this reflection matrix by using the symmetries and the boundary crossing equation. The cusp is introduced through a relative rotation between the two boundaries. Then the TBA trick of exchanging space and time leads to an exact equation for all values of L. The L=0 case corresponds to the cusped Wilson loop with no operators inserted. We then derive a slightly simplified integral equation which describes the small angle limit. We solve this equation up to three loops in perturbation theory and match the results that were obtained with more direct approaches.
The cusp anomalous dimension at three loops and beyond
We derive an analytic formula at three loops for the cusp anomalous dimension Gamma_cusp(phi) in N=4 super Yang-Mills. This is done by exploiting the relation of the latter to the Regge limit of massive amplitudes. We comment on the corresponding three loops quark anti-quark potential. Our result also determines a considerable part of the three-loop cusp anomalous dimension in QCD. Finally, we consider a limit in which only ladder diagrams contribute to physical observables. In that limit, a precise agreement with strong coupling is observed.
Constraining conformal field theories with a slightly broken higher spin symmetry
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.
Constraining conformal field theories with a higher spin symmetry
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.
From correlation functions to Wilson loops
We start with an n-point correlation function in a conformal gauge theory. We show that a special limit produces a polygonal Wilson loop with $n$ sides. The limit takes the $n$ points towards the vertices of a null polygonal Wilson loop such that successive distances $x^2_{i,i+1} \to 0$. This produces a fast moving particle that generates a "frame" for the Wilson loop. We explain in detail how the limit is approached, including some subtle effects from the propagation of a fast moving particle in the full interacting theory. We perform perturbative checks by doing explicit computations in N=4 super-Yang-Mills.
Einstein Gravity from Conformal Gravity
We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation. In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|Ψ[ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.