Found 2837 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Serre's genus 50 example

This note presents explicit equations (up to birational equivalence over $\mathbb{F}_2$) for a complete, smooth, absolutely irreducible curve $X$ over $\mathbb{F}_2$ of genus $50$ satisfying $#X(\mathbb{F}_2)=40$. Expand abstract.

This note presents explicit equations (up to birational equivalence over $\mathbb{F}_2$) for a complete, smooth, absolutely irreducible curve $X$ over $\mathbb{F}_2$ of genus $50$ satisfying $#X(\mathbb{F}_2)=40$. In his 1985 Harvard lecture notes on curves over finite fields, J-P.~Serre already showed the existence of such a curve: he used class

**field****theory**to describe the function**field**$\mathbb{F}_2(X)$ as a certain abelian extension of the function**field**$\mathbb{F}_2(E)$ of some elliptic curve $E/\mathbb{F}_2$. Although various more recent texts recall Serre's construction, explicit equations as well as a description of intermediate curves $X\to Y\to E$ over $\mathbb{F}_2$ seem to be new. We also describe explicit equations for a curve over $\mathbb{F}_2$ of genus $8$ with $11$ rational points, and for a curve over $\mathbb{F}_2$ of genus $22$ with $21$ rational points.8 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Covariant Momentum Map Thermodynamics for Parametrized **Field** **Theories**

We focus on the case of parametrized first-order field theories, as a concrete simplified model for fully constrained

**field****theories**sharing fundamental general covariant features with canonical general relativity. Expand abstract. Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a spacetime-covariant formalism for statistical mechanics and thermodynamics in the multi-symplectic framework for relativistic

**field****theories**. A general-covariant Gibbs state is derived, via a maximal entropy principle approach, in terms of the covariant momentum map associated with the lifted action of the diffeomorphisms group on the extended phase space of the**fields**. Such an equilibrium distribution induces a canonical spacetime foliation, with a Lie algebra-valued generalized notion of temperature associated to the covariant choice of a reference frame, and it describes a system of**fields**allowed to have non-vanishing probabilities of occupying states different from the diffeomorphism invariant configuration. We focus on the case of parametrized first-order**field**theories, as a concrete simplified model for fully constrained**field****theories**sharing fundamental general covariant features with canonical general relativity. In this setting, we investigate how physical equilibrium, hence time evolution, emerge from such a state via a gauge-fixing of the diffeomorphism symmetry.8 days ago

8/10 relevant

arXiv

8/10 relevant

arXiv

Pure and twisted holography

The holography is based on the two-dimensional N=2 supersymmetric Liouville conformal

**field****theory**that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. Expand abstract. We analyse a simple example of a holographically dual pair in which we topologically twist both

**theories**. The holography is based on the two-dimensional N=2 supersymmetric Liouville conformal**field****theory**that defines a unitary bulk quantum supergravity**theory**in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity**theory**in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configurations in the bulk supergravity**theory**and by quantising the solution space. Moreover, we note that the boundary calculation of the structure constants of the chiral ring carries over to the bulk**theory**as well. We thus construct a topological AdS/CFT duality in which the bulk**theory**is independent of the boundary metric.8 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Fundamental Physics, the Swampland of Effective **Field** **Theory** and Early
Universe Cosmology

I will argue that we need to go beyond effective

**field****theory**in order to understand the early universe, and that principles of superstring theory will yield a nonsingular cosmology. Expand abstract. Cosmological inflation is not the only early universe scenario consistent with current observational data. I will discuss the criteria for a successful early universe cosmology, compare a couple of the proposed scenarios (inflation, bouncing cosmologies, and the {\it emergent} scenario), focusing on how future observational data will be able to distinguish between them. I will argue that we need to go beyond effective

**field****theory**in order to understand the early universe, and that principles of superstring**theory**will yield a nonsingular cosmology.8 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Flat space holography and complex SYK

We derive the boundary action analogous to the Schwarzian as the key link between gravity and

**field****theory**sides and show that it coincides with a geometric action discovered recently by one of us, see 1908.08089. Expand abstract. We provide the first steps towards a flat space holographic correspondence in two bulk spacetime dimensions. The gravity side is described by a conformally transformed version of the matterless Callan-Giddings-Harvey-Strominger model. The

**field****theory**side follows from the complex Sachdev-Ye-Kitaev model in the limit of large specific heat and vanishing compressibility. We derive the boundary action analogous to the Schwarzian as the key link between gravity and**field****theory**sides and show that it coincides with a geometric action discovered recently by one of us, see 1908.08089.9 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

Monopole operators and their symmetries in QED3-Gross-Neveu models

The quantum critical point (QCP) for this transition is described by a conformal

**field****theory**: Compact quantum electrodynamics (QED3) with a fermionic self-interaction, a type of QED3-Gross-Neveu model. Expand abstract. Monopole operators are topological disorder operators in 2+1 dimensional compact gauge

**field****theories**appearing notably in quantum magnets with fractionalized excitations. For example, their proliferation in a spin-1/2 kagome Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin liquid phase to an antiferromagnet. The quantum critical point (QCP) for this transition is described by a conformal**field**theory: Compact quantum electrodynamics (QED3) with a fermionic self-interaction, a type of QED3-Gross-Neveu model. We obtain the scaling dimensions of monopole operators at the QCP using a state-operator correspondence and a large-N expansion, where 2N is the number of fermion flavors. We characterize the hierarchy of monopole operators at this SU(2) x SU(N) symmetric QCP.9 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Type-B Anomaly Matching and the 6D (2,0) **Theory**

We study type-B conformal anomalies associated with $\frac{1}{2}$-BPS Coulomb-branch operators in 4D $\mathcal N=2$ superconformal field theories. Expand abstract.

We study type-B conformal anomalies associated with $\frac{1}{2}$-BPS Coulomb-branch operators in 4D $\mathcal N=2$ superconformal

**field****theories**. When the vacuum preserves the conformal symmetry these anomalies coincide with the two-point function coefficients in the Coulomb-branch chiral ring. They are non-trivial functions of exactly-marginal couplings that can be determined from the $S^4$ partition function. In this paper, we examine the fate of these anomalies in vacua of the Higgs-branch moduli space, where conformal symmetry is spontaneously broken. We argue non-perturbatively that these anomalies are covariantly constant on conformal manifolds. In some cases, this can be used to show that they match in the broken and unbroken phases. Thus, we uncover a new class of data on the Higgs branch of 4D $\mathcal N=2$ conformal**field****theories**that are exactly computable. An interesting application of this matching occurs in $\mathcal N=2$ circular quivers that deconstruct the 6D (2,0)**theory**on a torus. In that context, we argue that 4D supersymmetric localisation can be used to calculate non-trivial data involving $\frac{1}{2}$-BPS operators of the 6D**theory**as exact functions of the complex structure of the torus.9 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

A Map Between Primordial Power Spectra and the Effective **Field** **Theory** of
Inflation

We have developed a precise dictionary between the spectrum of primordial density fluctuations and the parameters of the effective field theory (EFT) of inflation that determine the primordial power spectrum (PPS). Expand abstract.

We have developed a precise dictionary between the spectrum of primordial density fluctuations and the parameters of the effective

**field****theory**(EFT) of inflation that determine the primordial power spectrum (PPS). At lowest order the EFT contains two parameters: the slow-roll parameter $\epsilon$, which acts as an order parameter, and the speed of sound $c_s$. Applying second-order perturbation theory, we provide maps from the PPS to the EFT parameters that are precise up to the cube of the fractional change in the PPS $(\Delta \mathcal{P}/\mathcal{P})^3$, or less than $1\%$ for spectral features that modulate the PPS by $20\%$. While such features are not required when the underlying cosmological model is assumed to be $\Lambda$CDM they are necessary for alternative models that have no cosmological constant/dark energy. We verify the dictionary numerically and find those excursions in the slow-roll parameter that reproduce the PPS needed to fit Planck data for both $\Lambda$ and no-$\Lambda$ cosmological models.9 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

9 days ago

5/10 relevant

PhilSci

5/10 relevant

PhilSci

Unitary quantization of a charged scalar **field** and Schwinger effect

In this work, we apply the procedure developed for

**fields**in cosmological settings to analyze the quantization of a scalar**field**in the presence of an external electromagnetic classical field in a flat background. Expand abstract. Quantum

**field****theory**in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the**field**dynamics in the physical Hilbert space of the**theory**is a good criterion to ameliorate such ambiguity. Indeed, this criterion, together with a unitary implementation of the symmetries of the equations of motion, leads to a unique equivalence class of Fock representations. In this work, we apply the procedure developed for**fields**in cosmological settings to analyze the quantization of a scalar**field**in the presence of an external electromagnetic classical**field**in a flat background. We find a natural Fock representation that admits a unitary implementation of the quantum**field**dynamics. It automatically allows to define a particle number density at all times in the evolution with the correct asymptotic behavior, when the electric**field**vanishes. Moreover we show the unitary equivalence of all the quantizations that fulfill our criteria. Although we perform the**field**quantization in a specific gauge, we also show the equivalence between the procedures taken in different gauges.14 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv