Semiclassical Field Theory Research Articles

Stress inside the pion in holographic light-front QCD

In this work, we propose a method to compute the gravitational form factor D(Q2) in holographic QCD by exploiting the remarkable correspondence between semiclassical light-front QCD and semiclassical field theories in wrapped spacetime in five dimensions. The use of light-front holography bridges physics at large Q2 as attained in light-front QCD and physics at small Q2 where the coupling to scalar and tensor fields, e.g. glueballs, are dominant. As an application, we compute the D-term for the pion and compare the results with recent lattice simulations. Published by the American Physical Society 2024

On the origin of black hole paradoxes

Black hole firewall paradox is an inconsistency between four postulates in black hole physics: (1) the unitary evolution in quantum systems, (2) application of the semi-classical field theory in low curvature backgrounds, (3) statistical mechanical origin of the black hole entropy, and (4) the equivalence principle in the version of no drama for free-falling observers in the vicinity of the horizon. Based on the existence of the Hawking radiation for the static observers standing outside a Schwarzschild black hole, we show a direct contradiction between the postulates (2) and (4). If there is not a way out of this new problem, it implies the necessity of relaxing one of these two assumptions for resolving the black hole firewall paradox.

Heterotic strings on mathbbm{T} 3/ℤ2, Nikulin involutions and M-theory

We first describe the low energy dynamics of ten dimensional heterotic supergravity compactified on the smooth, flat 3-manifold mathbbm{T} 3/ℤ2, without supersymmetry, and explain how it arises from flat heterotic gauge fields. The semi-classical theory has both Coulomb and Higgs branches of non-supersymmetric vacua. We then give an exact worldsheet description as asymmetric orbifolds of mathbbm{T} 3, where the orbifold generator involves a Nikulin non-symplectic involution θ of the even self-dual lattice Γ(19,3). Along the way we briefly compare our findings with M-theory on K3/θ. Our construction gives a novel CFT description of the semi-classical field theory moduli space. In particular, the Wilson line parameters in the lattice I ⊂ Γ(19,3) of signature (19 − s, 1) which is invariant under θ, and in its orthogonal complement N , correspond respectively to Coulomb and Higgs branch moduli. There is a rich pattern of transitions amongst Higgs and Coulomb branches which we describe using the worldsheet theory.

Entanglement entropy and the large N expansion of two-dimensional Yang-Mills theory

Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large N. We calculate entanglement entropy in the 1/N expansion by mapping the theory to a system of N fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the “Boltzmann entropy,” log dim(R) per point of the entangling surface, which counts the number of distinct microstates, and the “Shannon entropy,” − Σ pR log pR, which captures fluctuations of the macroscopic state. We find that the entropy scales as N2 in the large N limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with N, and confirm this behaviour with numerical simulations. While the term of order N is surprising from the point of view of the string dual — in which only even powers of N appear in the partition function — we trace it to a breakdown of large N counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory.

Expectation values of coherent states for SU(2) Lattice Gauge Theories

This article investigates properties of semiclassical Gauge Field Theory Coherent States for general quantum gauge theories. Useful, e.g., for the canonical formulation of Lattice Gauge Theories these states are labelled by a point in the classical phase space and constructed such that the expectation values of the canonical operators are sharply peaked on said phase space point. For the case of the non-abelian gauge group SU(2), we will explicitly compute the expectation value of general polynomials including the first order quantum corrections. This allows asking more precise questions about the quantum fluctuations of any given semiclassical system.

How Can We Erase States Inside a Black Hole?

We investigate an entangled system, which is analogous to a composite system of a black hole and Hawking radiation. If Hawking radiation is well approximated by an outgoing particle generated from pair creation around the black hole, such a pair creation increases the total number of states. There should be a unitary mechanism to reduce the number of states inside the horizon for black hole evaporation. Because the infalling antiparticle has negative energy, as long as the infalling antiparticle finds its partner such that the two particles form a separable state, one can trace out such a zero energy system by maintaining unitarity. In this paper, based on some toy model calculations, we show that such a unitary tracing-out process is only possible before the Page time while it is impossible after the Page time. Hence, after the Page time, if we assume that the process is unitary and the Hawking pair forms a separable state, the internal number of states will monotonically increase, which is supported by the Almheiri-Marolf-Polchinski-Sully (AMPS) argument. In addition, the Hawking particles cannot generate randomness of the entire system; hence, the entanglement entropy cannot reach its maximum. Based on these results, we modify the correct form of the Page curve for the remnant picture. The most important conclusion is this: if we assume unitarity, semi-classical quantum field theory, and general relativity, then the black hole should violate the Bekenstein-Hawking entropy bound around the Page time at the latest; hence, the infinite production arguments for remnants might be applied for semi-classical black holes, which seems very problematic.

Emergent gravity from relatively local Hamiltonians and a possible resolution of the black hole information puzzle

In this paper, we study a possibility where gravity and time emerge from quantum matter. Within the Hilbert space of matter fields defined on a spatial manifold, we consider a sub-Hilbert space spanned by states which are parameterized by spatial metric. In those states, metric is introduced as a collective variable that controls local structures of entanglement. The underlying matter fields endow the states labeled by metric with an unambiguous inner product. Then we construct a Hamiltonian for the matter fields that is an endomorphism of the sub-Hilbert space, thereby inducing a quantum Hamiltonian of the metric. It is shown that there exists a matter Hamiltonian that induces the general relativity in the semi-classical field theory limit. Although the Hamiltonian is not local in the absolute sense, it has a weaker notion of locality, called relative locality : the range of interactions is set by the entanglement present in target states on which the Hamiltonian acts. In general, normalizable states are not invariant under the transformations generated by the Hamiltonian. As a result, a physical state spontaneously breaks the Hamiltonian constraint, and picks a moment of time. The subsequent flow of time can be understood as a Goldstone mode associated with the broken symmetry. The construction allows one to study dynamics of gravity from the perspective of matter fields. The Hawking radiation corresponds to a unitary evolution where entanglement across horizon is gradually transferred from color degrees of freedom to singlet degrees of freedom. The underlying quantum states remain pure as evaporating black holes keep entanglement with early Hawking radiations in the singlet sector which is not captured by the Bekenstein-Hawking entropy.

An AdS/EFT correspondence at large charge

Considering theories in sectors of large global charge Q results in a semiclassical effective field theory (eft) description for some strongly-coupled conformal field theories (cfts) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs.In this work we discuss the AdS/CFT correspondence in the regime Q≫CT≫1 where both the eft and gravity descriptions are valid and stable (CT being the central charge). We present the observation that the ground state energy as a function of the Abelian charge Q for a simple eft in some three-dimensional cfts coincides with the expression for the mass of an anti-de Sitter–Reissner–Nordström black hole as a function of its charge. Using this observation we propose a tentative dictionary relating cft, eft and holographic descriptions. We also find agreement for the higher-derivative corrections on both sides, suggesting a large-CT expansion on the eft side.

Pre-Hawking radiation cannot prevent the formation of apparent horizon

As an attempt to solve the black hole information loss paradox, recently there has been the suggestion that, due to semiclassical effects, a pre-Hawking radiation must exist during the gravitational collapse of matter, which in turn prevents the apparent horizon from forming. Assuming the pre-Hawking radiation does exist, here we argue the opposite. First we note that the stress energy tensor near the horizon for the pre-Hawking radiation is far too small to do anything to the motion of a collapsing shell. Thus the shell will always cross the apparent horizon within a finite proper time. Moreover, the amount of energy that can be radiated must be less than half of the total initial energy (if the particle starts at rest at infinity) before the shell becomes a null shell and cannot radiate any more without becoming tachyonic. We conclude that for any gravitational collapsing process within Einstein gravity and semiclassical quantum field theory, the formation of the apparent horizon is inevitable. Pre-Hawking radiation is therefore not a valid solution to the information paradox.

Entropy evolution of moving mirrors and the information loss problem

We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semi-classical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semi-classical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semi-classical quantum field theory.

A holographic model for black hole complementarity

We explore a version of black hole complementarity, where an approximate semiclassical effective field theory for interior infalling degrees of freedom emerges holographically from an exact evolution of exterior degrees of freedom. The infalling degrees of freedom have a complementary description in terms of outgoing Hawking radiation and must eventually decohere with respect to the exterior Hamiltonian, leading to a breakdown of the semiclassical description for an infaller. Trace distance is used to quantify the difference between the complementary time evolutions, and to define a decoherence time. We propose a dictionary where the evolution with respect to the bulk effective Hamiltonian corresponds to mean field evolution in the holographic theory. In a particular model for the holographic theory, which exhibits fast scrambling, the decoherence time coincides with the scrambling time. The results support the hypothesis that decoherence of the infalling holographic state and disruptive bulk effects near the curvature singularity are complementary descriptions of the same physics, which is an important step toward resolving the black hole information paradox.

Observing quantum gravity in asymptotically AdS space

The question is studied of whether an observer can discover quantum gravity in the semiclassical regime. It is shown that it is indeed possible to probe a certain quantum gravity effect by employing an appropriately designed detector. The effect is related to the possibility of having topologically inequivalent geometries in the path-integral approach at the same time. A conformal field theory (CFT) state which is expected to describe the eternal anti--de Sitter (AdS) black hole in the large-$N$ limit is discussed. It is argued under certain assumptions that the black hole boundary should be merely a patch of the entire AdS boundary. This leads then to a conclusion that that CFT state is the ordinary CFT vacuum restricted to that patch. If existent, the bulk CFT operators can behave as the ordinary semiclassical quantum field theory in the large-$N$ limit in the weak sense.

Bridging fermionic and bosonic short range entangled states

In this paper we construct bosonic short range entangled (SRE) states in all spatial dimensions by coupling a gauge field to fermionic SRE states with the same symmetries, and driving the gauge field to its confined phase. We demonstrate that this approach allows us to construct many examples of bosonic SRE states, and we demonstrate that the previous descriptions of bosonic SRE states such as the semiclassical nonlinear sigma model field theory and the Chern–Simons field theory can all be derived using the fermionic SRE states.

Black holes, entropies, and semiclassical spacetime in quantum gravity

We present a coherent picture of the quantum mechanics of black holes. The picture does not require the introduction of any drastically new physical effect beyond what is already known; it arises mostly from synthesizing and (re)interpreting existing results in appropriate manners. We identify the Bekenstein-Hawking entropy as the entropy associated with coarse-graining performed to obtain semiclassical field theory from a fundamental microscopic theory of quantum gravity. This clarifies the issues around the unitary evolution, the existence of the interior spacetime, and the thermodynamic nature in black hole physics--any result in semiclassical field theory is a statement about the maximally mixed ensemble of microscopic quantum states consistent with the specified background, within the precision allowed by quantum mechanics. We present a detailed analysis of information transfer in Hawking emission and black hole mining processes, clarifying what aspects of the underlying dynamics are (not) visible in semiclassical field theory. We also discuss relations between the black hole entropy and the entanglement entropy across the horizon. We then extend our discussions to more general contexts in quantum gravity. The subjects include extensions to de Sitter and Minkowski spaces and implications for complementarity and cosmology, especially the eternally inflating multiverse.

Anyon and loop braiding statistics in field theories with a topologicalΘterm

We demonstrate that the anyon statistics and three-loop statistics of various $2d$ and $3d$ topological phases can be derived using semiclassical nonlinear sigma model field theories with a topological $\ensuremath{\Theta}$ term. In our formalism, the braiding statistics has a natural geometric meaning: The braiding process of anyons or loops leads to a nontrivial field configuration in the space-time, which will contribute a braiding phase factor due to the $\ensuremath{\Theta}$ term.

Classical information transmission capacity of quantum black holes

The fate of classical information incident on a quantum black hole has been the subject of an ongoing controversy in theoretical physics, because a calculation within the framework of semi-classical curved-space quantum field theory appears to show that the incident information is irretrievably lost, in contradiction to time-honored principles such as time-reversibility and unitarity. Here, we show within this framework embedded in quantum communication theory that signaling from past to future null infinity in the presence of a Schwarzschild black hole can occur with arbitrary accuracy, and thus that classical information is not lost in black hole dynamics. The calculation relies on a treatment that is manifestly unitary from the outset, where probability conservation is guaranteed because black holes stimulate the emission of radiation in response to infalling matter. This stimulated radiation is non-thermal and contains all of the information about the infalling matter, while Hawking radiation contains none of it.

On Multi-Point Liouville Field Theory

In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or atleast require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field.

Is the firewall consistent? Gedanken experiments on black hole complementarity and firewall proposal

In this paper, we discuss the black hole complementarity and the firewall proposal at length. Black hole complementarity is inevitable if we assume the following five things: unitarity, entropy-area formula, existence of an information observer, semi-classical quantum field theory for an asymptotic observer, and the general relativity for an in-falling observer. However, large N rescaling and the AMPS argument show that black hole complementarity is inconsistent. To salvage the basic philosophy of the black hole complementarity, AMPS introduced a firewall around the horizon. According to large N rescaling, the firewall should be located close to the apparent horizon.We investigate the consistency of the firewall with the two critical conditions: the firewall should be near the time-like apparent horizon and it should not affect the future infinity. Concerning this, we have introduced a gravitational collapse with a false vacuum lump which can generate a spacetime structure with disconnected apparent horizons. This reveals a situation that there is a firewall outside of the event horizon, while the apparent horizon is absent. Therefore, the firewall, if it exists, not only does modify the general relativity for an in-falling observer, but also modify the semi-classical quantum field theory for an asymptotic observer.

Modeling polymerization of microtubules: A semi-classical nonlinear field theory approach

In this paper, for the first time, a three-dimensional treatment of microtubules’ polymerization is presented. Starting from fundamental biochemical reactions during microtubule’s assembly and disassembly processes, we systematically derive a nonlinear system of equations that determines the dynamics of microtubules in three dimensions. We found that the dynamics of a microtubule is mathematically expressed via a cubic-quintic nonlinear Schrödinger (NLS) equation. We show that in 3D a vortex filament, a generic solution of the NLS equation, exhibits linear growth/shrinkage in time as well as temporal fluctuations about some mean value which is qualitatively similar to the dynamic instability of microtubules. By solving equations numerically, we have found spatio-temporal patterns consistent with experimental observations.

Semi-Classical Quantum Fields Theories and Frobenius Manifolds

We show that a semi-classical quantum field theory comes with a versal family with the property that the corresponding partition function generates all path integrals., satisfies a system of second order differential equations determined by algebras of classical observables. This versal family gives rise to a notion of special coordinates that is analogous to that in string theories. We also show that for a large class of semi-classical theories, their moduli space has the structure of a Frobenius super-manifold.