arXiv subjects
Publications and source records attributed to De-liang Zhong.
We propose an analogue of the no particle production condition in two-dimensional anti-de Sitter space, and demonstrate how this criterion uniquely reconstructs the curved-space Liouville and Toda theories via general-multiplicity holographic correlators.
We consider type IIB string theory on $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathbb{T}^4$ in a large AdS radius expansion at arbitrary values of the relative RR and NS-NS fluxes. We develop a method for computing scaling dimensions in the dual CFT in this limit by combining a string field theory calculation, valid at finite quantized NS-NS flux but perturbative in RR flux, with a finite mixed-flux ansatz, which is constrained by worldsheet parity and motivated by classical string solutions. We apply the method to three families of states. In the pure-RR limit, our results agree both with a family of states computed using the worldsheet bootstrap and with another family computed using integrability.
We consider tree level scattering of gravitons in type IIA string theory on $AdS_4\times \mathbb{CP}^3$ to all orders in $α'$, which is dual to the stress tensor correlator in $U(N)_k\times U(N)_{-k}$ ABJM theory in the planar large $N$ limit and to all orders in large $λ\sim N/k$. The small curvature expansion of this correlator, defined via a Borel transform, is given by the flat space Virasoro-Shapiro amplitude plus AdS curvature corrections. We fix curvature corrections by demanding that their resonances are consistent with the superconformal block expansion of the correlator and with a worldsheet ansatz in terms of single-valued multiple polylogarithms. The first correction is fully fixed in this way, and matches independent results from integrability, as well as the $R^4$ correction at finite AdS curvature that was previously fixed using supersymmetric localization. We are also able to fix the second curvature correction by using a few additional assumptions, and find that it also satisfies various non-trivial consistency checks. We use our results to fix the tree level $D^4R^4$ correction at finite AdS curvature, and to give many predictions for future integrability studies.
We investigate the quantum entanglement of Bethe states across a family of integrable spin chains, including the XXX$_{\frac{1}{2}}$ model, its higher-spin generalizations (XXX$_s$), and the non-compact $SL(2,\mathbb{R})$ chain. For on-shell eigenstates, we perform a comprehensive scan of the bipartite entanglement entropy across the entire spectrum of finite chains with periodic boundary conditions, and identify the Bethe solutions that minimize and maximize the entanglement. These extremal solutions follow systematic, spin-dependent patterns in the Bethe quantum numbers. In the XXX$_{\frac{1}{2}}$ spin chain, for the antiferromagnetic chain, the state with minimal entropy always coincides with the lowest-energy state (the ground state) within a given fixed-magnon sector. For the higher-spin XXX$_s$ model, however, the lowest-entropy state is not always identical to the ground state, and can even be the state of highest energy. By contrast, the Bethe roots that maximize entropy exhibit considerably more intricate structure. Our analysis further reveals how special Bethe root configurations, such as singular and strange solutions, affect entanglement, and it uncovers characteristic entanglement features in the non-compact $SL(2,\mathbb{R})$ chain that are absent from compact spin chains. For off-shell Bethe states, we develop an optimization algorithm that extremizes the entanglement entropy over rapidity distributions, enabling us to explore the maximum entanglement achievable by a Bethe state without imposing the Bethe ansatz equations.
We compute the AdS Veneziano amplitude for type IIB gluon scattering in $AdS_5 \times S^3$ to all orders in $α'$ in a small curvature expansion. This is achieved by combining a dispersion relation in the dual $4d$ $\mathcal{N}=2$ SCFT with an ansatz for the amplitude as a worldsheet integral in terms of multiple polylogarithms. The first curvature correction is fully fixed in this way and satisfies consistency checks in the high energy limit, the low energy expansion as previously fixed using supersymmetric localisation, and for the energy of massive string operators, which we independently compute using a semiclassical expansion. We also combine localisation with this first curvature correction to fix the unprotected $D^4F^4$ correction to the amplitude at finite curvature.
We study the first curvature correction to the string amplitude of four Kaluza--Klein (KK) modes on $AdS_3 \times S^3 \times M_4$, with $M_4=K3$ or $T^4$, in type IIB string theory, which is holographically dual to the four--point correlator $\langle \mathcal{O}_{p_1} \mathcal{O}_{p_2} \mathcal{O}_{p_3} \mathcal{O}_{p_4} \rangle$ of certain half--BPS operators in the boundary D1--D5 CFT. The result takes the form of an integral over the Riemann sphere, analogous to the flat-space Virasoro--Shapiro amplitude, but with insertions of single-valued multiple polylogarithms of weight three. Our results are obtained in two steps. First, we derive the $AdS_3 \times S^3$ Virasoro--Shapiro amplitude in the special case $\langle \mathcal{O}_{p} \mathcal{O}_{p} \mathcal{O}_{1} \mathcal{O}_{1} \rangle$, by matching the CFT block expansion with an ansatz based on single-valued multiple polylogarithms. We then employ the $AdS \times S$ Mellin formalism to generalize the result to the general case of four arbitrary KK modes $\langle \mathcal{O}_{p_1} \mathcal{O}_{p_2} \mathcal{O}_{p_3} \mathcal{O}_{p_4} \rangle$. Our analysis yields an infinite set of results for operator anomalous dimensions and OPE data in D1--D5 CFT at strong coupling. In particular, the resulting scaling dimensions of certain operators are shown to be consistent with classical string theory computations.
We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several examples and compare them against existing data for the four-point function of the displacement operator. Additionally, we provide a few new predictions that extend the current understanding of these correlators.
We compute the AdS Virasoro-Shapiro amplitude for scattering of dilatons in type IIB string theory with pure RR flux on $AdS_3\times S^3\times M_4$ for $M_4=T^4$ or $K3$, to all orders in $α'$ in a small AdS curvature expansion. This is achieved by comparing the flat space limit of the dual D1D5 CFT correlator to an ansatz for the amplitude as a worldsheet integral in terms of single valued multiple polylogarithms. The first curvature correction is fully fixed in this way, and satisfies consistency checks in the high energy limit, and by comparison of the energy of massive string operators to a semiclassical expansion. Our result gives infinite predictions for CFT data in the planar limit at strong coupling, which can guide future integrability studies.
We introduce new diagnostics of the transition between the ergodic and many-body localization phases, which are based on complexity measures defined via the probability distribution function of the Lanczos coefficients of the tri-diagonalized Hamiltonian. We use these complexity measures to analyze the power-law random banded matrix model as a function of the correlation strength and show that the moments and the entropy of the distribution diagnose the ergodic to many-body transition, as well as the distinctive feature of the phases concerning the memory of the initial conditions.
We study a class of renormalization group flows on line defects that can be described by a generalized free field with ordered planar contractions on the line. They are realized, for example, in large $N$ gauge theories with matter in the fundamental representation and arise generically in non-relativistic CFTs. We analyze the flow exactly and compute the change in the $g$-function between the UV and IR fixed points. We relate the result to the change in the two-point function of the displacement operator and check the monotonicity of the defect entropy along the flow analytically. Finally, we give a general realization of this type of flow starting from the direct sum of the IR fixed point and a trivial line. This type of defect renormalization group flow parallels the well-studied case of double-trace flow.
The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large $N$ holographic theories, these fundamental observables are dual to the open string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions -- conformal invariance of the line defect, large $N$ factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.
We study mesonic line operators in Chern-Simons theories with bosonic or fermionic matter in the fundamental representation. In this paper, we elaborate on the classification and properties of these operators using all loop resummation of large $N$ perturbation theory. We show that these theories possess two conformal line operators in the fundamental representation. One is a stable renormalization group fixed point, while the other is unstable. They satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two mesonic line operators. The boundary operators on which the lines can end are classified by their conformal dimension and transverse spin, which we compute explicitly at finite 't Hooft coupling. We match the operators in the bosonic and fermionic theories.
We study Chern-Simons theories at large $N$ with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators.
We initiate the study of $T\bar T$-like irrelevant solvable deformations in quantum field theory with boundaries and defects. For this purpose, we employ a general formalism developed in the context of spin chains, which allows us to derive both, the deformed bulk and boundary/defect scattering matrices of integrable models. Using the deformed scattering matrices, we derive the flow equation for the deformed finite volume spectrum, as well as the cylinder partition function and the exact $g$-function.
We consider four-point integrals arising in the planar limit of the conformal "fishnet" theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in $AdS_{3}\times S^{1}$, in a generalized scaling combining the thermodynamic and short-distance limits.
We present the TBA equations and the Y-system for the exact spectrum of general multi-magnon local operators in the $D$-dimensional anisotropic version of the bi-scalar fishnet CFT. The mixing matrix of such operators is given in terms of fishnet planar graphs of multi-wheel and multi-spiral type. These graphs probe the two main building blocks of the TBA approach that are the magnon dispersion relation and the magnon scattering matrix and which we both obtain by diagonalising suitable graph-building operators. We also obtain the dual version of the TBA equations, which relates, in the continuum limit, $D$-dimensional graphs to two dimensional sigma models in $AdS_{D+1}$. It allows us to verify a general formula obtained by A.~Zamolodchikov for the critical coupling.
We consider structure constants of single-trace operators at strong coupling in planar $\mathcal{N}=4$ SYM theory using the hexagon formalism. We concentrate on heavy-heavy-light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.
We initiate the study of four-point functions of large BPS operators at any value of the coupling. We do it by casting it as a sum over exchange of superconformal primaries and computing the structure constants using integrability. Along the way, we incorporate the nested Bethe ansatz structure to the hexagon formalism for the three-point functions and obtain a compact formula for the asymptotic structure constant of a non-BPS operator in a higher rank sector.