arXiv subjects

Song He

Publications and source records attributed to Song He.

At least 91 records · Page 5Linked to original sources

arXiv2024

Holographic stress tensor correlators on higher genus Riemann surfaces

In this work, we present a comprehensive study of holographic stress tensor correlators on general Riemann surfaces, extending beyond the previously well-studied torus cases to explore higher genus conformal field theories (CFTs) within the framework of the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We develop a methodological approach to compute holographic stress tensor correlators, employing the Schottky uniformization technique to address the handlebody solutions for higher genus Riemann surfaces. Through rigorous calculations, we derive four-point stress tensor correlators, alongside recurrence relations for higher-point correlators, within the $\mathrm{AdS}_3/\mathrm{CFT}_2$ context. Additionally, our research delves into the holography of cutoff $\mathrm{AdS}_3$ spaces, offering novel insights into the lower-point correlators of the $T\bar{T}$-deformed theories on higher genus Riemann surfaces up to the first deformation order.

hep-th↗

arXiv2024

From squared amplitudes to energy correlators

The leading order $N$-point energy correlators of maximally supersymmetric Yang-Mills theory in the limit where the $N$ detectors are collinear can be expressed as an integral of the $1\to N$ splitting function, which is given by the $(N{+}3)$-point squared super-amplitudes at tree level. This provides yet another example that the integrand of certain physical observable -- $N$-point energy correlator -- is computed by the canonical form of a positive geometry -- the (tree-level) "squared amplituhedron". By extracting such squared amplitudes from the $f$-graph construction, we compute the integrand of energy correlators up to $N=11$ and reveal new structures to all $N$; we also show important properties of the integrand such as soft and multi-collinear limits. Finally, we take a first look at integrations by studying possible residues of the integrand: our analysis shows that while this gives prefactors in front of multiple polylogarithm functions of $N=3,4$, the first unknown case of $N=5$ already involves elliptic polylogarithmic functions with many distinct elliptic curves, and more complicated curves and higher-dimensional varieties appear for $N>5$.

hep-th↗

arXiv2024

Differential equations and recursive solutions for cosmological amplitudes

Recently considerable efforts have been devoted to computing cosmological correlators and the corresponding wavefunction coefficients, as well as understanding their analytical structures. In this note, we revisit the computation of these ``cosmological amplitudes" associated with any tree or loop graph for conformal scalars with time-dependent interactions in the power-law FRW universe, directly in terms of iterated time integrals. We start by decomposing any such cosmological amplitude (for loop graph, the ``integrand" prior to loop integrations) as a linear combination of {\it basic time integrals}, one for each {\it directed graph}. We derive remarkably simple first-order differential equations involving such time integrals with edges ``contracted" one at a time, which can be solved recursively and the solution takes the form of Euler-Mellin integrals/generalized hypergeometric functions. By combining such equations, we then derive a complete system of differential equations for all time integrals needed for a given graph. Our method works for any graph: for a tree graph with $n$ nodes, this system can be transformed into the {\it canonical differential equations} of size $4^{n{-}1}$ quivalent to the graphic rules derived recently%so-called ``kinematic flow", and we also derive the system of differential equations for loop integrands {\it e.g.} of all-loop two-site graphs and one-loop $n$-gon graphs. Finally, we show how the differential equations truncate for the de Sitter (dS) case (in a way similar to differential equations for Feynman integrals truncate for integer dimensions), which immediately yields the complete symbol for the dS amplitude with interesting structures {\it e.g.} for $n$-site chains and $n$-gon cases.

hep-th↗

arXiv2024

Supergluon scattering in AdS: constructibility, spinning amplitudes, and new structures

We elaborate on a new recursive method proposed in arXiv:2312.15484 for computing tree-level $n$-point supergluon amplitudes as well as those with one gluon, i.e., spinning amplitudes, in ${\rm AdS}_5 \times S^3$. We present an improved proof for the so-called "constructibility" of supergluon and spinning amplitudes based on their factorizations and flat-space limit, which allows us to determine these amplitudes in Mellin space to all $n$. We present explicit and remarkably simple expressions for up to $n=7$ supergluon amplitudes and $n=6$ spinning amplitudes, which can be viewed as AdS generalizations of the scalar-scaffolded gluon amplitudes proposed recently. We then reveal a series of hidden structures of these AdS amplitudes including (1) an understanding of general pole structures especially the precise truncation on descendent poles (2) a derivation of simple "Feynman rules" for the all-$n$ amplitudes with the simplest R-symmetry structures, and (3) certain universal behavior analogous to the soft/collinear limit of flat-space amplitudes.

hep-th↗

arXiv2024

Spacetime with prescribed hidden symmetry

In this paper, we investigate spacetime characterized by a hidden symmetry defined by a given Killing tensor. To exhibit this hidden symmetry, the inverse metric must commute with the Killing tensor under the Schouten-Nijenhuis bracket, which translates into a system of partial differential equations (PDEs) for the inverse metric. For some significant examples, we solve these PDEs directly, deriving spacetimes with prescribed hidden symmetries, including those specified by higher-rank Killing tensors. Utilizing the hidden symmetries, we study related problems such as null geodesics, photon region, and separation of variables of wave equations. Through this work, we aim to demonstrate that hidden symmetry is more accessible than previously believed.

gr-qc↗

arXiv2024

Constraints on holographic QCD phase transitions from PTA observations

The underlying physics of QCD phase transition in the early Universe remains largely unknown due to its strong-coupling nature during the quark-gluon plasma/hadron gas transition, yet a holographic model has been proposed to quantitatively fit the lattice QCD data while with its duration of the first-order phase transition (FoPT) left undetermined. At specific baryon chemical potential, the first-order QCD phase transition agrees with the observational constraint of baryon asymmetry. It, therefore, provides a scenario for phase transition gravitational waves (GWs) within the Standard Model of particle physics. If these background GWs could contribute dominantly to the recently claimed common-spectrum red noise from pulsar timing array (PTA) observations, the duration of this FoPT can be well constrained, and the associated primordial black holes are still allowed by current observations.

hep-ph↗

arXiv2024

Entanglement and Pseudo Entanglement Dynamics versus Fusion in CFT

The fusion rules and operator product expansion (OPE) serve as crucial tools in the study of operator algebras within conformal field theory (CFT). Building upon the vision of using entanglement to explore the connections between fusion coefficients and OPE coefficients, we employ the replica method and Schmidt decomposition method to investigate the time evolution of entanglement entropy (EE) and pseudo entropy (PE) for linear combinations of operators in rational conformal field theory (RCFT). We obtain a formula that links fusion coefficients, quantum dimensions, and OPE coefficients. We also identify two definition schemes for linear combination operators. Under one scheme, the EE captures information solely for the heaviest operators, while the PE retains information for all operators, reflecting the phenomenon of pseudo entropy amplification. Irrespective of the scheme employed, the EE demonstrates a step-like evolution, illustrating the effectiveness of the quasiparticle propagation picture for the general superposition of locally excited states in RCFT. From the perspective of quasiparticle propagation, we observe spontaneous block-diagonalization of the reduced density matrix of a subsystem when quasiparticles enter the subsystem.

hep-th↗

arXiv2024

Note on holographic torus stress tensor correlators in $AdS_3$ gravity

In the AdS$_3$/CFT$_2$ framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/$T\bar{T}$-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system's dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

hep-th↗

arXiv2024

Holographic torus correlators in $\text{AdS}_3$ gravity coupled to scalar field

This paper investigates holographic torus correlators of generic operators at conformal infinity and a finite cutoff within AdS$_3$ gravity coupled with a free scalar field. Using a near-boundary analysis and solving the gravitational boundary value problem, we solve Einstein's equation and calculate mixed correlators for massless and massive coupled scalar fields. The conformal ward identity on the torus has been reproduced holographically, which can be regarded as a consistency check. Further, recurrence relations for a specific class of higher-point correlators are derived, validating AdS$_3$/CFT$_2$ with non-trivial boundary topology. While the two-point scalar correlator is accurately computed on the thermal AdS$_3$ saddle, the higher-point correlators associated with scalar and stress tensor operators are explored.

hep-th↗

arXiv2024

Revisiting holographic model for thermal and dense QCD with a critical point

To quantitatively provide reliable predictions for the hot and dense QCD matter, a holographic model should be adjusted to describe first-principles lattice results available at vanishing baryon chemical potential. The equation of state from two well-known lattice groups, the HotQCD collaboration and the Wuppertal-Budapest (WB) collaboration, shows visible differences at high temperatures. We revisit the Einstein-Maxwell-dilaton (EMD) holographic model for hot QCD with 2+1 flavors and physical quark masses by fitting lattice QCD data from the WB collaboration. Using the parameterization for the scalar potential and gauge coupling proposed in our work [Phys.Rev.D 106 (2022) 12, L121902], the equation of state, the higher order baryon number susceptibilities, and the chiral condensates are in quantitative agreement with state-of-the-art lattice results. We find that the critical endpoint (CEP) obtained from fitting the WB collaboration data is nearly identical to the one from the HotQCD collaboration, suggesting the robustness of the location of the CEP. Moreover, our holographic prediction for the CEP location is in accord with more recent Bayesian analysis on a large number of holographic EMD models and an effective potential approach of QCD from gap equations.

hep-ph↗

arXiv2024

Irrelevant and marginal deformed BMS field theories

In this study, we investigate various deformations within the framework of Bondi-van der Burg-Metzner-Sachs invariant field theory (BMSFT). Specifically, we explore the impact of Bondi-van der Burg-Metzner-Sachs (BMS) symmetry on the theory by introducing key deformations, namely, $T \overline{T}$, $JT_μ$, and $\sqrt{T \overline{T}}$ deformations. In the context of generic seed theories possessing BMS symmetry, we derive the first-order correction of correlation functions using the systematic application of BMS symmetry ward identities. However, it is worth noting that higher-order corrections are intricately dependent on the specific characteristics of the seed theories. To illustrate our findings, we select the BMS free scalar and free fermion as representative seed theories. We then proceed to analytically determine the deformed action by solving the nontrivial flow equations. Additionally, we extend our analysis to include second-order deformations within these deformed theories.

hep-th↗

arXiv2024

Island formula in Planck brane

Double holography offers a profound understanding of the island formula by describing a gravitational system on AdS$_d$ coupled to a conformal field theory on $\mathbb{R}^{1,d-1}$, dual to an AdS$_{d+1}$ spacetime with an end-of-the-world (EOW) brane. In this work, we extend the proposal in [A. Almheiri et al. JHEP 03 (2020) 149] by considering that the dual bulk spacetime has two EOW branes: one with a gravitational system and the other with a thermal bath. We demonstrate an equivalence between this proposal and the wedge holographic theory. We examine it in both Anti-de Sitter gravity and de Sitter gravity by calculating the entanglement entropy of the Hawking radiation. Finally, we employ the doubly holographic model to verify the formula for the entanglement entropy in a subregion within conformally flat spacetime.

hep-th↗

arXiv2024

Pseudo-entropy for descendant operators in two-dimensional conformal field theories

We study the late-time behaviors of pseudo-(Rényi) entropy of locally excited states in rational conformal field theories (RCFTs). To construct the transition matrix, we utilize two non-orthogonal locally excited states that are created by the application of different descendant operators to the vacuum. We show that when two descendant operators are generated by a single Virasoro generator acting on the same primary operator, the late-time excess of pseudo-entropy and pseudo-Rényi entropy corresponds to the logarithmic of the quantum dimension of the associated primary operator, in agreement with the case of entanglement entropy. However, for linear combination operators generated by the generic summation of Virasoro generators, we obtain a distinct late-time excess formula for the pseudo-(Rényi) entropy compared to that for (Rényi) entanglement entropy. As the mixing of holomorphic and antiholomorphic generators enhances the entanglement, in this case, the pseudo-(Rényi) entropy can receive an additional contribution. The additional contribution can be expressed as the pseudo-(Rényi) entropy of an effective transition matrix in a finite-dimensional Hilbert space.

hep-th↗

arXiv2024

Holographic Euclidean thermal correlator

In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and $U(1)$ current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein's gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for $U(1)$ current and stress tensor in the scalar and shear channels.

hep-th↗

arXiv2024

Gravitational Waves and Primordial Black Hole Productions from Gluodynamics by Holography

Understanding the nature of quantum chromodynamics (QCD) matter is important but challenging due to the presence of non-perturbative dynamics under extreme conditions. We construct a holographic model describing the gluon sector of QCD at finite temperatures in the non-perturbative regime. The equation of state as a function of temperature is in good accordance with the lattice QCD data. Moreover, the Polyakov loop and the gluon condensation, which are proper order parameters to capture the deconfinement phase transition, also agree quantitatively well with the lattice QCD data. We obtain a strong first-order confinement/deconfinement phase transition at $T_c=276.5\,\text{MeV}$ that is consistent with the lattice QCD prediction. Based on our model for a pure gluon hidden sector, we compute the stochastic gravitational waves and primordial black hole (PBH) productions from this confinement/deconfinement phase transition in the early Universe. The resulting stochastic gravitational-wave backgrounds are found to be within detectability in the International Pulsar Timing Array and Square Kilometre Array in the near future when the associated productions of PBHs saturate the current observational bounds on the PBH abundances from the LIGO-Virgo-Collaboration O3 data.

hep-ph↗

arXiv2024

Phase structure and critical phenomena in 2-flavor QCD by holography

We explore the phase structure of Quantum Chromodynamics (QCD) with two dynamical quark flavors at finite temperature and baryon chemical potential, employing the non-perturbative gauge/gravity duality approach. Our gravitational model is tailored to align with state-of-the-art lattice data regarding the thermal properties of multi-flavor QCD. Following a rigorous parameter calibration to match equations of state and the QCD trace anomaly at zero chemical potential derived from cutting-edge lattice QCD simulations, we investigate thermodynamic quantities and order parameters. We predict the location of the critical endpoint (CEP) at $(μ_{\text{CEP}}, T_{\text{CEP}})=(219,182)$ MeV at which a line of first-order phase transitions terminate. We compute critical exponents associated with the CEP and find that they almost coincide with the critical exponents of the quantum 3D Ising model.

hep-ph↗

arXiv2023

On symbology and differential equations of Feynman integrals from Schubert analysis

We take the first step in generalizing the so-called "Schubert analysis", originally proposed in twistor space for four-dimensional kinematics, to the study of symbol letters and more detailed information on canonical differential equations for Feynman integral families in general dimensions with general masses. The basic idea is to work in embedding space and compute possible cross-ratios built from (Lorentz products of) maximal cut solutions for all integrals in the family. We demonstrate the power of the method using the most general one-loop integrals, as well as various two-loop planar integral families (such as sunrise, double-triangle and double-box) in general dimensions. Not only can we obtain all symbol letters as cross-ratios from maximal-cut solutions, but we also reproduce entries in the canonical differential equations satisfied by a basis of dlog integrals.

hep-th↗

arXiv2023

Holographic renormalized Entanglement and entropic $c-$function

We compute holographic entanglement entropy (EE) and the renormalized EE in AdS solitons with gauge potential for various dimensions. The renormalized EE is a cutoff-independent universal component of EE. Via Kaluza-Klein compactification of $S^1$ and considering the low-energy regime, we deduce the $(d-1)$-dimensional renormalized EE from the odd-dimensional counterpart. This corresponds to the shrinking circle of AdS solitons, probed at large $l$. The minimal surface transitions from disk to cylinder dominance as $l$ increases. The quantum phase transition occurs at a critical subregion size, with renormalized EE showing non-monotonic behavior around this size. Across dimensions, massive modes decouple at lower energy, while degrees of freedom with Wilson lines contribute at smaller energy scales.

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