arXiv subjects

Hongliang Jiang

Publications and source records attributed to Hongliang Jiang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Spin Thresholds, RG Flows, and Minimality in 4D $\mathcal{N}=2$ QFT

Long ago, Argyres and Douglas discovered a particularly simple interacting 4D $\mathcal{N}=2$ superconformal field theory (SCFT) on the Coulomb branch of $SU(3)$ $\mathcal{N}=2$ super Yang-Mills. Further hints of the theory's simplicity arise due to the fact that it has the smallest possible value of the $c$ central charge among unitary interacting $\mathcal{N}=2$ SCFTs. A main purpose of this note is to uncover additional aspects of this minimal Argyres-Douglas (MAD) theory's simplicity. In particular, we argue that: (1) the MAD theory shares an infinite set of large spin thresholds in part of its operator spectrum with the free $\mathcal{N}=2$ Maxwell theory (this data is therefore invariant under generic $\mathcal{N}=2$-preserving renormalization group flows to the IR) and (2) the MAD theory has, at every order in the natural grading, the smallest number of "Schur" operators of any unitary $\mathcal{N}=2$ theory (interacting or free). We then show that property (1) has a suitable generalization for all $(A_1, A_{2k})$ cousins of the MAD theory. In particular, the corresponding large spin thresholds encode generic renormalization group flows within this class. This construction therefore gives a different handle on these flows from the one provided by the Seiberg-Witten description. To emphasize the importance of these spin thresholds, we abstractly study theories with "enough matter" to form Higgs branches and argue that infinitely many spin thresholds are small or vanishing.

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arXiv2021

Celestial OPEs and $ w_{1+\infty}$ algebra from worldsheet in string theory

Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with $\mathcal N=1$ and $\mathcal N=2$ worldsheet supersymmetry. In the case of $\mathcal N=2$ string, we also derive all the $\overline{SL (2,\mathbb R)}$ descendant contributions in the celestial OPE; the soft sector of such OPE just yields the $w_{1+\infty}$ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the realization of celestial holography in string theory.

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arXiv2021

1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds

We systematically study 4D $\mathcal{N}=2$ superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in $\mathbb{C}^4$. We show that if a theory in this class has no $\mathcal{N}=2$-preserving exactly marginal deformation (i.e., the theory is isolated as an $\mathcal{N}=2$ SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the $a$ and $c$ central charges, this condition implies that IHS theories satisfying $a<{1\over24}(15r+2f)$ and $c<{1\over6}(3r+f)$ (where $r$ is the complex dimension of the Coulomb branch, and $f$ is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $\mathcal{N}=2$ SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

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arXiv2021

Celestial superamplitude in $\mathcal N=4$ SYM theory

Celestial amplitude is a new reformulation of momentum space scattering amplitude and offers a promising way for flat holography. In this paper, we study the celestial amplitude in $\mathcal N=4$ Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $\mathcal N=4$ SYM theory. We also compute the three-point and four-point celestial super-amplitude explicitly. They can be identified as the correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $\mathcal N=4$ SYM amplitude via 2D celestial conformal field theory.

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arXiv2020

Swing surfaces and holographic entanglement beyond AdS/CFT

We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. Flat$_3$/BMSFT is a candidate of holography for asymptotically flat three-dimensional spacetimes, while (W)AdS$_3$/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

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arXiv2020

Modular Hamiltonians in flat holography and (W)AdS/WCFT

We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS$_3$ or AdS$_3$ backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on "modular chaos" introduced recently in the context of the AdS/CFT correspondence.

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arXiv2020

Entanglement Entropy in Flat Holography

BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.

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arXiv2020

$\mathcal N=2$ Supersymmetry Deformations, Electromagnetic Duality and Dirac-Born-Infeld Actions

We study the general deformation of $\mathcal N=2$ supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the $SU(2)$ R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of $\mathcal N=2\to \mathcal N=1$ supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-linearly realised, described by a nilpotent constraint on the deformed $\mathcal N=2$ chiral-chiral superfield. We show that the generic magnetic deformation induces an ordinary FI D-term along the linear supersymmetry via the theta-angle. Moreover, we argue that the resulting action differs on-shell from the standard one (DBI+FI) by fermionic contributions.

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arXiv2020

Note on supersymmetric Dirac-Born-Infeld action with Fayet-Iliopoulos term

We study the Dirac-Born-Infeld (DBI) action with one linear and one non-linear supersymmetry in the presence of a constant Fayet-Iliopoulos (FI) D-term added explicitly or through a deformation of supersymmetry transformations. The linear supersymmetry appears to be spontaneously broken since the D auxiliary field gets a non-vanishing vacuum expectation value and an extra term proportional to the FI parameter involving fermions emerges in the non-linear formulation of the action written recently. However in this note, we show that on-shell this action is equivalent to a standard supersymmetric DBI action ${\it without}$ FI term but with redefined tension, at least up to order of mass-dimension 12 effective interactions.

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arXiv2020

Magnetic Deformation of Super-Maxwell Theory in Supergravity

A necessary condition for partial breaking of N=2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest of these deformations which already occurs in N=1 global supersymmetry, and its coupling to supergravity. It can be viewed as an imaginary constant shift of the D-auxiliary real field of an abelian gauge multiplet. We show how this deformation describes the magnetic dual of a Fayet-Iliopoulos term, a result that remains valid in supergravity, using its new-minimal formulation. Local supersymmetry and the deformation induce a positive cosmological constant. Moreover, the deformed U(1) Maxwell theory coupled to supergravity describes upon elimination of the auxiliary fields the gauging of R-symmetry, realised by the Freedman model of 1976. To this end, we construct the chiral spinor multiplet in superconformal tensor calculus by working out explicitly its transformation rules and use it for an alternative description of the new-minimal supergravity coupled to a U(1) multiplet. We also discuss the deformed Maxwell theory in curved superspace.

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arXiv2020

Boundary correlators in WZW model on AdS$_2$

Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS$_2$ have a particularly simple structure. For example, the correlators of the Liouville scalar happen to be the same as the correlators of the chiral component of the stress tensor on a plane restricted to the real line. Here we show that an analogous relation is true also in the WZW model: boundary correlators of the WZW scalars have the same structure as the correlators of chiral Kač-Moody currents. This is checked at the level of the tree and one-loop Witten diagrams in AdS$_2$. We also compute some tree-level correlators in a generic $σ$-model defined on AdS$_2$ and show that they simplify only in the WZW case where an extra Kač-Moody symmetry appears. In particular, the terms in 4-point correlators having logarithmic dependence on 1d cross-ratio cancel only at the WZW point. One motivation behind this work is to learn how to compute AdS$_2$ loop corrections in 2d models with derivative interactions related to the study of correlators of operators on Wilson loops in string theory in AdS.

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arXiv2020

Supersymmetric Liouville theory in AdS$_2$ and AdS/CFT

In a series of recent papers, a special kind of AdS$_2$/CFT$_1$ duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS$_2$ background are the same as the correlators of the corresponding primary operators in the chiral half of that 2d CFT in flat space restricted to the real line. The examples considered were: (i) the Liouville theory where the operator dual to the Liouville scalar in AdS$_2$ is the stress tensor; (ii) the abelian Toda theory where the operators dual to the Toda scalars are the $\mathcal W$-algebra generators; (iii) the non-abelian Toda theory where the Liouville field is dual to the stress tensor while the extra gauged WZW theory scalars are dual to non-abelian parafermionic operators. By direct Witten diagram computations in AdS$_2$ one can check that the structure of the boundary correlators is indeed consistent with the Virasoro (or higher) symmetry. Here we consider a supersymmetric generalization: the $\mathcal N=1$ superconformal Liouville theory in AdS$_2$. We start with the super Liouville theory coupled to 2d supergravity and show that a consistent restriction to rigid AdS$_2$ background requires a non-zero value of the supergravity auxiliary field and thus a modification of the Liouville potential from its familiar flat-space form. We show that the Liouville scalar and its fermionic partner are dual to the chiral half of the stress tensor and the supercurrent of the super Liouville theory on the plane. We perform tests supporting the duality by explicitly computing AdS$_2$ Witten diagrams with bosonic and fermionic loops.

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arXiv2019

$T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry

We investigate the behaviour of two-dimensional quantum field theories with $\mathcal{N}=(0,2)$ supersymmetry under a deformation induced by the `$T\bar{T}$' composite operator. We show that the deforming operator can be defined by a point-splitting regularisation in such a way as to preserve $\mathcal{N}=(0,2)$ supersymmetry. As an example of this construction, we work out the deformation of a free $\mathcal{N}=(0,2)$ theory and compare to that induced by the Noether stress-energy tensor. Finally, we show that the $\mathcal{N}=(0,2)$ supersymmetric deformed action actually possesses $\mathcal{N}=(2,2)$ symmetry, half of which is non-linearly realised.

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arXiv2019

Supersymmetric $J\bar{T}$ and $T\bar{J}$ deformations

We explore the $J\bar{T}$ and $T\bar{J}$ deformations of two-dimensional field theories possessing $\mathcal N=(0,1),(1,1)$ and $(0,2)$ supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the $J\bar{T}/T\bar{J}$ deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional $J\bar T /T\bar J$ operator on-shell. We also present some examples of $J\bar T /T\bar J$ flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.

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arXiv2019

Non-Linear Supersymmetry and $T\bar T$-like Flows

The $T\bar{T}$ deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain $\mathcal N =(2,2)$ models in two dimensions, where we observe an intriguing similarity with known $\mathcal N=1 $ models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from $T\bar{T}$-like flow equations. We show that in four dimensions this is indeed the case for $\mathcal N=1 $ Born-Infeld theory, as well as for the Goldstino action for spontaneously broken $\mathcal N=1 $ supersymmetry.

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arXiv2019

Non-abelian Toda theory on AdS$_2$ and AdS$_2$/CFT$_2^{1/2}$ duality

It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS$_2$ background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS$_2$ are directly related to the correlation functions of the chiral $\mathcal W$-symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS$_2$/CFT$_1$ duality where the CFT$_1$ is the chiral half of a 2d CFT; we shall refer to this as AdS$_{2}$/CFT$^{1/2}_{2}$. In this paper we demonstrate that this duality applies also to the non-abelian Toda theory containing a Liouville scalar coupled to a 2d $σ$-model originating from the $SL(2, \mathbb R)/U(1)$ gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor $T$ while the other two scalars are dual to the parafermionic operators $V^\pm$ of the non-abelian Toda CFT. We explicitly check the duality at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of $(T, V^+,V^-)$ (computed using a free field representation) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS$_{2}$.

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arXiv2019

Anomalous Gravitation and its Positivity from Entanglement

We explore the emergence of gravitation from entanglement in holographic CFTs with gravitational anomalies. More specifically, the holographic correspondence between topologically massive gravity (TMG) with gravitational Chern-Simons term in the 3D bulk and its dual CFT with unbalanced left and right moving central charges on the 2D boundary, is studied from the quantum entanglement perspective. Using the first law of entanglement, we derive the holographic dictionary of the energy-momentum tensor in TMG, including the chiral case with logarithmic mode. Furthermore, we show that the linearized equation of motion of TMG can also be obtained from entanglement using the Wald-Tachikawa covariant phase space formalism. Finally, we identify a quasi-local gravitational energy in the entanglement wedge as the holographic dual of relative entropy in gravitationally anomalous CFTs. The positivity and monotonicity of relative entropy imply that such a gravitational energy should be positive definite and become larger when increasing the size of the entanglement wedge. These constraints from quantum information may be potentially used to discuss the UV inconsistent issues of TMG.

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arXiv2017

Massive Fields as Systematics for Single Field Inflation

During inflation, massive fields can contribute to the power spectrum of curvature perturbation via a dimension-5 operator. This contribution can be considered as a bias for the program of using $n_s$ and $r$ to select inflation models. Even the dimension-5 operator is suppressed by $Λ= M_p$, there is still a significant shift on the $n_s$-$r$ diagram if the massive fields have $m\sim H$. On the other hand, if the heavy degree of freedom appears only at the same energy scale as the suppression scale of the dimension-5 operator, then significant shift on the $n_s$-$r$ diagram takes place at $m=Λ\sim 70H$, which is around the inflationary time-translation symmetry breaking scale. Hence, the systematics from massive fields pose a greater challenge for future high precision experiments for inflationary model selection. This result can be thought of as the impact of UV sensitivity to inflationary observables.

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