Found 2962 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Proof of the quantum null energy condition for free fermionic **field**
**theories**

The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. Expand abstract.

The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. The QNEC states that $\langle T_{kk}\rangle_{p}\geq lim_{A\rightarrow 0}\left(\frac{\hbar}{2\pi A}S_{out}^{\prime\prime}\right)$ where $S_{out}$ is the entanglement entropy restricted to one side of a codimension-2 surface $\Sigma$ which is deformed in the null direction about a neighborhood of point $p$ with area $A$. A proof of QNEC has been given which applies to free and super-renormalizable bosonic

**field**theories, and to any points that lie on a stationary null surface. Using similar assumptions and method, we prove the QNEC for fermionic**field****theories**.57 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

A mathematical framework to compare classical **field** **theories**

To construct the mathematical framework, a mathematical category (in the sense of category theory) in which a versatile comparison becomes possible is sought and the geometric

**theory**of partial differential equations is used to define what can be understood by a correspondence between**theories**and by an intersection... Expand abstract. This article is a summary of the Master's thesis I wrote under the supervision of Prof. Ion Stamatescu and Prof. James Weatherall as a result of more than a year of research. The original work contained a bit more than 140 pages, while in the present summary all less relevant topics were shifted to the appendix such that the main part does not exceed 46 pages to ease the reading. However, the appendix was kept in order to show which parts were omitted. In the article, a mathematical framework to relate and compare any classical

**field****theories**is constructed. A classical**field****theory**is here understood to be a**theory**that can be described by a (possibly non-linear) system of partial differential equations and thus the notion includes but is not limited to classical (Newtonian) mechanics, hydrodynamics, electrodynamics, the laws of thermodynamics, special and general relativity, classical Yang-Mills**theory**and so on. To construct the mathematical framework, a mathematical category (in the sense of category theory) in which a versatile comparison becomes possible is sought and the geometric**theory**of partial differential equations is used to define what can be understood by a correspondence between**theories**and by an intersection of two**theories**under such a correspondence. This is used to define in a precise sense when it is meaningful to say that two**theories**share structure and a procedure (based on formal integrability) is introduced that permits to decide whether such structure does in fact exist or not if a correspondence is given. It is described why this framework is useful both for conceptual and practical purposes and how to apply it. As an example, the**theory**is applied to electrodynamics and, among other things, magneto-statics is shown to share structure with a subtheory of hydrodynamics.59 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Zero-point energies, dark matter, and dark energy

A quantum field theory has finite zero-point energy if the sum over all boson modes $b$ of the $n$th power of the boson mass $ m_b^n $ equals the sum over all fermion modes $f$ of the $n$th power of the fermion mass $ m_f^n $ for $n= 0$, 2, and 4. Expand abstract.

A quantum

**field****theory**has finite zero-point energy if the sum over all boson modes $b$ of the $n$th power of the boson mass $ m_b^n $ equals the sum over all fermion modes $f$ of the $n$th power of the fermion mass $ m_f^n $ for $n= 0$, 2, and 4. The zero-point energy of a**theory**that satisfies these three conditions with otherwise random masses is huge compared to the density of dark energy. But if in addition to satisfying these conditions, the sum of $m_b^4 \log m_b/\mu$ over all boson modes $b$ equals the sum of $ m_f^4 \log m_f/\mu $ over all fermion modes $f$, then the zero-point energy of the**theory**is zero. The value of the mass parameter $\mu$ is irrelevant in view of the third condition ($n=4$). The particles of the standard model do not remotely obey any of these four conditions. But an inclusive**theory**that describes the particles of the standard model, the particles of dark matter, and all particles that have not yet been detected might satisfy all four conditions if pseudomasses are associated with the mean values in the vacuum of the divergences of the interactions of the inclusive model. Dark energy then would be the finite potential energy of the inclusive**theory**.59 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Towards a conformal **field** **theory** for Schramm-Loewner evolutions

We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal

**field****theory**. Expand abstract. We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal

**field****theory**. Both are closely related to crossing probabilities and interfaces in critical models in two-dimensional statistical mechanics. We gather and supplement previous results with different perspectives, point out remaining difficulties, and suggest directions for future studies.60 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Quantitative estimates in stochastic homogenization for correlated
coefficient **fields**

This paper is about the homogenization of linear elliptic operators in divergence form with stationary random coefficients that have only slowly decaying correlations. Expand abstract.

This paper is about the homogenization of linear elliptic operators in divergence form with stationary random coefficients that have only slowly decaying correlations. It deduces optimal estimates of the homogenization error from optimal growth estimates of the (extended) corrector. In line with the heuristics, there are transitions at dimension $d=2$, and for a correlation-decay exponent $\beta=2$; we capture the correct power of logarithms coming from these two sources of criticality. The decay of correlations is sharply encoded in terms of a multiscale logarithmic Sobolev inequality (LSI) for the ensemble under consideration --- the results would fail if correlation decay were encoded in terms of an $\alpha$-mixing condition. Among other ensembles popular in modelling of random media, this class includes coefficient

**fields**that are local transformations of stationary Gaussian**fields**. The optimal growth of the corrector $\phi$ is derived from bounding the size of spatial averages $F=\int g\cdot\nabla\phi $ of its gradient. This in turn is done by a (deterministic) sensitivity estimate of $F$, that is, by estimating the functional derivative $\frac{\partial F}{\partial a}$ of $F$ w.~r.~t.~the coefficient**field**$a$. Appealing to the LSI in form of concentration of measure yields a stochastic estimate on $F$. The sensitivity argument relies on a large-scale Schauder**theory**for the heterogeneous elliptic operator $-\nabla\cdot a\nabla$. The treatment allows for non-symmetric $a$ and for systems like linear elasticity.61 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Dispersionless Integrable Hierarchy via Kodaira-Spencer Gravity

We describe a BV framework of effective

**field****theories**that leads to the B-model interpretation of dispersionless integrable hierarchy. Expand abstract. We explain how dispersionless integrable hierarchy in 2d topological

**field****theory**arises from the Kodaira-Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the current observables associated to the infinite abelian symmetries of the Kodaira-Spencer gravity. We describe a BV framework of effective**field****theories**that leads to the B-model interpretation of dispersionless integrable hierarchy.61 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Genus **theory** and Euclidean ideals for real biquadratic **fields**

In this paper, we use the theory of genus fields to study the Euclidean ideals of certain real biquadratic fields $K.$ Comparing with the previous works, our methods yield a new larger family of real biquadratic fields $K$ having Euclidean ideals; and the conditions for our family seem to be more efficient for the computations. Expand abstract.

In this paper, we use the

**theory**of genus**fields**to study the Euclidean ideals of certain real biquadratic**fields**$K.$ Comparing with the previous works, our methods yield a new larger family of real biquadratic**fields**$K$ having Euclidean ideals; and the conditions for our family seem to be more efficient for the computations. Moreover, the previous approaches mainly focus on the case if $h_K=2$, while the present approach can also deal with the general case when $h_K=2^t (t\geq1)$, where $h_K$ denotes the ideal class number of $K$. In particular, if $h_K\geq 4$, it shows that $H(K)$, the Hilbert class**field**of $K$, is always non-abelian over $\mathbb{Q}$ for the family of $K$ given in this paper having Euclidean ideals, whereas the previous approaches always requires that $H(K)$ is abelian over $\mathbb{Q}$ explicitly or implicitly. Finally, some open questions have also been listed for further research.62 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

Anomaly Obstructions to Symmetry Preserving Gapped Phases

Anomalies are renormalization group invariants that constrain the dynamics of quantum field theories. Expand abstract.

Anomalies are renormalization group invariants that constrain the dynamics of quantum

**field****theories**. We show that certain anomalies for discrete global symmetries imply that the underlying**theory**either spontaneously breaks its generalized global symmetry or is gapless. We identify an obstruction, formulated in terms of the anomaly inflow action, that must vanish if a symmetry preserving gapped phase, i.e. a unitary topological quantum**field**theory, exits with the given anomaly. Our result is similar to the $2d$ Lieb-Schultz-Mattis theorem but applies more broadly to continuum**theories**in general spacetime dimension with various types of discrete symmetries including higher-form global symmetries. As a particular application, we use our result to prove that certain $4d$ non-abelian gauge**theories**at $\theta=\pi$ cannot flow at long distances to a phase which simultaneously, preserves time-reversal symmetry, is confining, and is gapped. We also apply our obstruction to $4d$ adjoint QCD and constrain its dynamics.63 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Superconformal algebras and holomorphic **field** **theories**

We compute the holomorphic twists of four-dimensional superconformal algebras, and argue that the resulting algebras act naturally by holomorphic vector fields on holomorphically twisted superconformal theories. Expand abstract.

We compute the holomorphic twists of four-dimensional superconformal algebras, and argue that the resulting algebras act naturally by holomorphic vector

**fields**on holomorphically twisted superconformal**theories**. We demonstrate that this symmetry enhances to the action of an infinite-dimensional local Lie algebra, the Dolbeault resolution of all holomorphic vector**fields**on a punctured superspace. Global symmetries also enhance to the Dolbeault resolution of holomorphic functions valued in the Lie algebra; at the classical level, both of these higher symmetry algebras act naturally on the holomorphic twist of any Lagrangian theory, whether superconformal or not. We show that these algebras are related to two-dimensional chiral algebras extracted from four-dimensional superconformal**theories**in recent work; further deforming the differential induces the Koszul resolution of a plane in $\mathbb{C}^2$, and the cohomology of the higher symmetry algebras are the usual Virasoro and Kac-Moody chiral algebras. We show that the central extensions of those chiral algebras arise from recently studied central extensions of our higher symmetry algebras. However, the higher algebras admit many further deformations not originating in the global superconformal algebra; these localize to any smooth complex curve in $\mathbb{C}^2$, resolving the holomorphic vector**fields**there, and expect that they will lead to even more exotic behavior in the case of singular or nonreduced curves. We consider explicit examples of $\mathcal{N}=2$ gauge theories, and demonstrate that an anomaly to realizing the higher symmetry algebra at the quantum level vanishes precisely when the**theory**is, in fact, superconformal; for such theories, we also give an explicit description of the chiral algebras that result after further deformation.64 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

Anomalies of QFTs from M-**theory** and Holography

We describe a systematic way of computing the 't Hooft anomalies for continuous symmetries of Quantum Field Theories in even dimensions that can be geometrically engineered from M5-branes. Expand abstract.

We describe a systematic way of computing the 't Hooft anomalies for continuous symmetries of Quantum

**Field****Theories**in even dimensions that can be geometrically engineered from M5-branes. Our approach is based on anomaly inflow, and characterizes the anomaly polynomial of the QFT in terms of the geometric definition of the**field****theory**. In particular, when the QFT admits a holographic dual, the topological data of the solution is sufficient to compute the anomalies of the dual**field**theory, including finite terms in $N$. We study several classes of examples in four and six dimensions, with or without known M5-brane probe configurations.64 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv