arXiv subjects

Jia Tian

Publications and source records attributed to Jia Tian.

30 records · Page 2Linked to original sources

arXiv2021

Baby universes, ensemble averages and factorizations with matters

We investigate 2D topological gravity theories with matter fields turned on. We compute correlators of boundary creation operators with extra matter insertions. We provide a systematic procedure to determine a set of $α$-states on which the correlation functions of the different boundary operators factorize. Our results suggest that the boundary dual is an ensemble average of theories with different numbers of replicas of a seed matter contribution that is represented by excitations on top of the gravity sector. The construction of the $α$-states and the subsequent computations in the Hilbert space point of view are most conveniently done when the bulk couplings of the matter fields are expanded in a basis of vortices, which can be thought of as a 1-dimensional analogue of the SD-branes. We further demonstrate the existence of null states and the conditions imposed by reflection positivity. Moreover, in the CGS model with only disk and cylinder topologies, we map the baby universe creation and annihilation operators to the coupling constants in the one time SYK model, which allows us to match the wormhole and half-wormhole contributions in the CGS model explicitly to those identified in the SYK model. This explicitly realizes Coleman's initial idea. Some details of the computations in a variety of concrete models are presented.

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arXiv2021

$λ$-deformed $AdS_5\times S^5$ superstring from 4D Chern-Simons theory

We present the construction of the $λ$-deformation of $AdS_5\times S^5$ superstring from the four dimensional Chern-Simons-type gauge theory. The procedure is applicable to all the semi-symmetric coset models and generalizes the previous construction of $λ$-deformation of the symmetric coset models.

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arXiv2021

Note on the nonrelativistic $T\bar{T}$ deformation

In this paper, we present our study on the $T\bar{T}$-deformation of non-relativistic complex scalar field theory. We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics. Furthermore we compute the exact energy spectrum of the deformed free theory by using the Brillouin-Wigner perturbation theory in an appropriate regularization scheme.

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arXiv2021

Deformed Integrable Models from Holomorphic Chern-Simons Theory

We study the approaches to two-dimensional integrable field theories via a six-dimensional(6D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a four-dimensional Chern-Simons theory, while under solving along fibres it leads to four-dimensional(4D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both four-dimensional theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several two-dimensional integrable deformations in this framework. We find that the $λ$-deformation, the rational $η$-deformation and the generalized $λ$-deformation can not be realized from 4D integrable model approach, even though they could be obtained from 4D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of $λ$-deformation and the $η$-deformation in the trigonometric description could be obtained from the 6D theory in both ways, by considering the case that $(3,0)$-form in the 6D theory is allowed to have zeros.

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arXiv2021

Lax Connections in $T\bar{T}$-deformed Integrable Field Theories

In this work, we try to construct the Lax connections of $T\bar{T}$-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the $T\bar{T}$-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.

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arXiv2020

Separation of variables in the WZW models

We consider dynamics of scalar and vector fields on gravitational backgrounds of the Wess-Zumino-Witten models. For SO(4) and its cosets, we demonstrate full separation of variables for all fields and find a close analogy with a similar separation of vector equations in the backgrounds of the Myers--Perry black holes. For SO(5) and higher groups separation of variables is found only in some subsectors.

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arXiv2020

Meta-Learning across Meta-Tasks for Few-Shot Learning

Existing meta-learning based few-shot learning (FSL) methods typically adopt an episodic training strategy whereby each episode contains a meta-task. Across episodes, these tasks are sampled randomly and their relationships are ignored. In this paper, we argue that the inter-meta-task relationships should be exploited and those tasks are sampled strategically to assist in meta-learning. Specifically, we consider the relationships defined over two types of meta-task pairs and propose different strategies to exploit them. (1) Two meta-tasks with disjoint sets of classes: this pair is interesting because it is reminiscent of the relationship between the source seen classes and target unseen classes, featured with domain gap caused by class differences. A novel learning objective termed meta-domain adaptation (MDA) is proposed to make the meta-learned model more robust to the domain gap. (2) Two meta-tasks with identical sets of classes: this pair is useful because it can be employed to learn models that are robust against poorly sampled few-shots. To that end, a novel meta-knowledge distillation (MKD) objective is formulated. There are some mistakes in the experiments. We thus choose to withdraw this paper.

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arXiv2020

Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories

In this work, we study the line and loop operators in three-dimensional ${\mathcal N}=2$ fishnet theories in detail. We construct the straight line and circular loop operators which are at least classically half-BPS. We develop a new regularization scheme at frame $-1$ which is suitable for the study of the fermionic BPS loops in general super-Chern-Simons-matter theories. We initialize the perturbative computation for the vacuum expectation values of the circular BPS loop operators based on this scheme. We construct the cusped line operators as well, and compute the vacuum expectation values of these cusped line operators up to two-loop order. We find that the universal cusp anomalous dimension vanishes, if we put aside the fact that the generalized potential has a double pole in the $1/ε$ expansion.

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arXiv2020

Comments on $λ$--deformed models from 4D Chern-Simons theory

We study the $λ$--deformation of symmetric coset models from the viewpoint of a four dimensional Chern-Simons theory \cite{CY3}. In addition, by applying the "dual" boundary conditions of the ones used in the construction $η$--deformed PCM in the trigonometric description \cite{TRIGYB} we construct a $λ$--deformation type model.

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arXiv2020

Notes on index of quantum integrability

A quantum integrability index was proposed in \cite{KMS}. It systematizes the Goldschmidt and Witten's operator counting argument \cite{GW} by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models ${SU(N)}/{SO(N)}$ and $SO(2N)/{SO(N)\times SO(N)}$. The indexes of these theories are all non-positive except for the case of ${SO(4)}/{SO(2)\times SO(2)}$. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the $\mathbb{CP}^N$ model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.

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arXiv2019

Asymmetric $λ$-deformed cosets

We study the integrable asymmetric $λ$-deformations of the $SO(n+1)/SO(n)$ coset models, following the prescription proposed in \cite{AsyLambda}. We construct all corresponding deformed geometries in an inductive way. Remarkably we find a $Z_2$ transformation which maps the asymmetric $λ$--deformed models to the symmetric $λ$--deformed models.

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arXiv2019

Holographic Correlators on Integrable Superstrata

In this work, we study the $\frac{1}{8}$-BPS heavy-heavy-light-light correlators in the D1D5 CFT and its holographic dual. On the field theory side, we compute the fermionic four-point correlators at the free orbifold point. On the dual gravity side, we compute the correlators of the scalar operators in the supergravity limit of the D1D5 CFT. Following the strategy of \cite{Galliani:2017jlg}, the four-point function is converted into a two-point function in non-trivial geometries known as superstrata which are supergravity solutions preserving $1/8$ supersymmetries. We focus on a family of integrable superstrata, which allows us to compute the correlators perturbatively.

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