Bilocal Field Research Articles

Bilocal holography and locality in the bulk

Bilocal holography provides a constructive approach to the vector model/higher spin gravity duality. It has two ingredients: a change of field variables and a change of space time coordinates. The change of field variables ensures that the loop expansion parameter becomes 1N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N} $$\\end{document}. The change of coordinates solves the Clebsch-Gordan problem of moving from the tensor product basis (in which the collective bilocal field is written) to the direct sum basis (appropriate for the description of the gravity fields). We argue that the change of space time coordinates can be deduced by requiring that operators constructed in the bilocal collective field theory are dual to local operators in the AdS bulk.

Bilocal Field Theory for Composite Scalar Bosons.

We give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu-Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, ϕ(r→), in the center-of-mass frame that satisfies a Schrödinger-Klein-Gordon equation with eigenvalues m2. We analyze the "coloron" model (single perturbative massive gluon exchange) which yields a UV completion of the NJL model. This has a BCS-like enhancement of its interaction, ∝Nc the number of colors, and is classically critical with gcritical remarkably close to the NJL quantum critical coupling. Negative eigenvalues for m2 lead to spontaneous symmetry breaking, and the Yukawa coupling of the bound state to constituent fermions is emergent.

Meson spectrum of SU(2) QCD1+1 with quarks in Large representations

We consider SU(2) quantum chromodynamics in 1 + 1 dimensions with a single quark in the spin J representation of the gauge group and study the theory in the large J limit where the gauge coupling g2 → 0 and J → ∞ with λ = g2J2 fixed. We work with a Dirac spinor field for arbitrary J, and with a Majorana spinor for integer J since the integer spin representations of SU(2) are real, and analyze the two cases separately.The theory is reformulated in terms of global colour non-singlet fermion bilocal operators which satisfy a W∞ × U(2J + 1) algebra. In the large J limit, the dynamics of the bilocal fields is captured by fluctuations along a particular coadjoint orbit of the W∞ algebra. We show that the global colour-singlet sector of the bilocal field fluctuations satisfy the same integral equation for meson wavefunctions that appears in the ’t Hooft model. For Majorana spinors in the integer spin J representation, the Majorana condition projects out half of the meson spectrum, as a result of which the linear spacing of the asymptotic meson spectrum for Majorana fermions is double that of Dirac fermions. The Majorana condition also projects out the zero mass bound state that is present for the Dirac quark at zero quark mass.We also consider the formulation of the model in terms of local charge densities and compute the quark spectral function in the large J limit: we see evidence for the absence of a pole in the quark propagator.

Semiclassical dynamics of Hawking radiation

We consider gravity in 3+1 spacetime dimensions coupled to N scalar matter fields in a semiclassical limit where . The dynamical evolution of a black hole including the back-reaction of the Hawking radiation on the metric is formulated as an initial-value problem. The quantum stress-energy tensor is evaluated using a point-splitting regularization along spacelike geodesics. To account for the quantum entanglement of the matter fields, they are treated as a set of bilocal collective fields defined on spacelike hypersurfaces. The resulting semiclassical field equations include terms up to fourth order in derivatives that can be treated in a perturbative expansion. The formulation we arrive at should be amenable to numerical simulation of time-dependent semiclassical spacetime.

Quantum interference of hydrodynamic modes in a dirty marginal Fermi liquid

We study the electrical transport of a two-dimensional non-Fermi liquid with disorder, and we determine the first quantum correction to the semiclassical dc conductivity due to quantum interference. We consider a system with $N$ flavors of fermions coupled to SU($N$) critical matrix bosons. Motivated by the SYK model, we employ the bilocal field formalism and derive a set of finite-temperature saddle-point equations governing the fermionic and bosonic self-energies in the large-$N$ limit. Interestingly, disorder smearing induces a marginal Fermi liquid (MFL) self-energy for the fermions. We next consider fluctuations around the saddle points and derive a MFL-Finkel'stein nonlinear sigma model. We find that the Altshuler-Aronov quantum conductance correction gives linear-$T$ resistivity that can dominate over the Drude result at low temperature. The strong temperature dependence of the quantum correction arises due to rapid relaxation of the mediating quantum-critical bosons. We verify that our calculations explicitly satisfy the Ward identity at the semiclassical and quantum levels. Our results establish that quantum interference persists in two-particle hydrodynamic modes, even when quasiparticles are subject to strong (Planckian) dissipation.

Factorizing wormholes in a partially disorder-averaged SYK model

In this paper, we introduce a “partially disorder-averaged” SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as “half” of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the “half-wormholes” which were found in recent studies. We find that the large N saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.

Bi-local fields interacting with a constant electric field and related problems including the Schwinger effect

The bi-local fields are the quantum fields of two-particle systems, the bi-local systems, bounded by relativistic potentials. Since those form constrained dynamical systems, it is limited to introduce the interactions of the bi-local fields with other fields. In this paper, the interaction between the bi-local fields and a constant electric field E is studied with consideration for the consistency of constraints. Then, we evaluate the Schwinger effect for the bi-local systems, which gives the pair production probability of the bound states as a function of the charges of respective particles and the coupling constant in the binding potential. Through this analysis, we also discuss the possibility for the dissociation of bi-local systems due to the electric field.

Reconceptualizing the Haitian Migration System in the Caribbean Basin: A Spatial Approach to Multi‐local Fields

AbstractThis article addresses the issue of Haitian migration in the Caribbean basin from a geodynamic point of view—that is to say, by focusing on the spatial dynamics of migratory flows that integrate societies of origin, settlement, and transit within the same framework. It approaches the geographies of Haitian mobility by situating the bilocal transnational migration field in the larger framework of the multilocal, global Haitian migration system. Transnational fields interconnect to weave a Caribbean system of migration and circulation. The observation of individuals’ mobility patterns in this diasporic system reveals the strategic role of regional hubs (Miami, St. Martin, etc.), in which Caribbean migration fields (those that connect Haiti to the rest of the region) and extra‐Caribbean mobility fields (i.e., intra‐US or transatlantic fields) are interconnected.

Constructing the bulk at the critical point of three-dimensional large N vector theories

In the context of the AdS4/CFT3 correspondence between higher spin fields and vector theories, we use the constructive bilocal fields based approach to this correspondence, to demonstrate, at the IR critical point of the interacting vector theory and directly in the bulk, the removal of the Δ=1 (s=0) state from the higher spins field spectrum, and to exhibit simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher spin fields are obtained in a simple manner from boundary bilocals, by the change of variables previously derived for the UV critical point (in momentum space), together with a field redefinition.

A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model

We review our recent work [1] where we studied the chaotic property of the two coupled Sachdev-Ye-Kitaev systems exhibiting a Hawking-Page like phase transition. By computing the out-of-time-ordered correlator in the large NN limit by using the bilocal field formalism, we found that the chaos exponent of this model shows a discontinuous fall-off at the phase transition temperature. Hence in this model the Hawking-Page like transition is correlated with a transition in chaoticity, as expected from the relation between a black hole geometry and the chaotic behavior in the dual field theory.

A classical mechanical model of two interacting massless particles in de Sitter space and its quantization

A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a way that the resulting, generalized action reduces to the original action in a limit that de Sitter radius goes to infinity. We analyze the Hamiltonian formulation in accordance with Dirac's prescription for constrained Hamiltonian systems and carry out its subsequent canonical quantization in coordinate representation following DeWitt. As the result, we derive a fourth-order differential wave equation for bilocal fields that, in the infinite radius limit, reproduces one obtained in the original model for Minkowski space case.

A derivation of AdS/CFT for vector models

We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev’s classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.

Nuclear Decay Oscillations and Nonlinear Quantum Dynamics

Several experimental groups reported the evidence of periodic modulations of nuclear decay constants which amplitudes are of the order $${{10}^{{ - 3}}}$$ and periods of one year, 24 h or about one month. We argue that such deviations from radioactive decay law can be described in nonlinear quantum mechanics framework, in which decay process obeys to nonlinear Shrodinger equation with Doebner–Goldin terms. Possible corrections to Hamiltonian of quantum system interaction with gravitation field considered, it’s shown that they correspond to some emergent gravity theories, in particular, bilocal field model. It’s shown that proposed model describes decay parameter variations which agree with experimental results for Po-214 $$\alpha $$ -decay life-time oscillations.

A model of quantum gravity with emergent spacetime

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial sites. In the limit that the size of the matrix is large, the sites can collectively form a spatial manifold. The manifold is determined from the pattern of entanglement present across local Hilbert spaces associated with column vectors of the matrix. With no structure of manifold fixed in the background, the spacetime gauge symmetry is generalized to a group that includes diffeomorphism in arbitrary dimensions. The momentum and Hamiltonian that generate the generalized diffeomorphism obey a first-class constraint algebra at the quantum level. In the classical limit, the constraint algebra of the general relativity is reproduced as a special case. The first-class nature of the algebra allows one to express the projection of a quantum state of the matrix to a gauge invariant state as a path integration of dynamical variables that describe collective fluctuations of the matrix. The collective variables describe dynamics of emergent spacetime, where multi-fingered times arise as Lagrangian multipliers that enforce the gauge constraints. If the quantum state has a local structure of entanglement, a smooth spacetime with well-defined dimension, topology, signature and geometry emerges at the saddle-point, and the spin two mode that determines the geometry can be identified. We find a saddle-point solution that describes a series of (3 + 1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between. The phase transitions between spacetimes with different signatures are caused by Lifshitz transitions in which the pattern of entanglement is rearranged across the system. Fluctuations of the collective variables are described by bi-local fields that propagate in the spacetime set up by the saddle-point solution.

Manifest non-locality in quantum mechanics, quantum field theory and quantum gravity

We summarize our recent work on the foundational aspects of string theory as a quantum theory of gravity. We emphasize the hidden quantum geometry (modular spacetime) behind the generic representation of quantum theory and then stress that the same geometric structure underlies a manifestly T-duality covariant formulation of string theory, that we call metastring theory. We also discuss an effective non-commutative description of closed strings implied by intrinsic non-commutativity of closed string theory. This fundamental non-commutativity is explicit in the metastring formulation of quantum gravity. Finally we comment on the new concept of metaparticles inherent to such an effective non-commutative description in terms of bi-local quantum fields.

Notes on the Syk Model in Real Time

Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it diverges after the transformation to the fermion bilocal fields. We point out that the generating functional of the SYK model in real time is well defined even after the transformation to the bilocal fields and it can be used for nonperturbative investigations of its properties. The SYK model in zero dimensions is studied, its large N expansion is evaluated and phase transitions are investigated.

Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction

We study the three dimensional O(N) invariant bosonic vector model with a frac{lambda }{N}{left({phi}^a{phi}^aright)}^2 interaction at its infrared fixed point, using a bilocal field approach and in an 1/N expansion. We identify a (negative energy squared) bound state in its spectrum about the large N conformal background. At the critical point this is identified with the Δ = 2 state. We further demonstrate that at the critical point the Δ = 1 state disappears from the spectrum.

Bilocal fields and gravity

We study a classical bilocal field theory perturbatively up to second-order. The chosen theory is the simplest which incorporates action-at-a-distance, while keeping nonlocal effects short-ranged. We show that the new degrees of freedom introduced by bilocality can be interpreted as gravitational degrees of freedom in the following sense: solutions of the bilocal system at linear and second-orders contain as a subset, gravitational perturbations (spacetime fluctuations) also to that order. In other words, gravity can be thought to originate in a bilocal field theory. We examine potential implications.

On 1/N diagrammatics in the SYK model beyond the conformal limit

In the present work we discuss aspects of the 1/N expansion in the SYK model, formulated in terms of the semiclassical expansion of the bilocal field path integral. We derive cutting rules, which are applicable for all planar vertices in the bilocal field diagrams. We show that these cutting rules lead to novel identities on higher-point correlators, which could be used to constrain their form beyond the solvable conformal limit. We also demonstrate how the cutting rules can simplify the computation of amplitudes on an example of the six-point function.

On replica-nondiagonal large N saddles in the SYK model

We study the saddle points of the SYK model, formulated in terms of the replica bilocal fields, beyond the replica-diagonal assumption. We find a family of replica-nondiagonal saddle points in the IR limit, where the saddle point equations are separable. We use the Parisi ansatz to find the replicanondiagonal solutions and take the replica limit. The free energy on these solutions is computed, and we find that some of the replica-nondiagonal saddles have lower free energy than the replica-diagonal saddle point.