Symmetries of the N=4 SYM S-matrix

Symmetries of the Bosonic String S-Matrix

The bracket operation on mutually local BRST classes may be combined with Lorentz invariance and analyticity to write an infinite set of finite difference relations on string scattering amplitudes. When combined with some simple physical criteria these relations uniquely determine the genus zero string $S$-matrix for $N\leq 26$-particle scattering in $\IR^{25,1}$ in terms of a single parameter, $κ$, the string coupling. We propose that the high-energy limit of the relations are the Ward identities for the high-energy symmetries of string theory.

Additional symmetries of KP, Grassmannian, and the string equation II

As in the first part of this paper (hep-th 9204092), solutions to a string equation are regarded as fixed points of some additional symmetries of a hierarchy of integrable equations. In this part matrix hierarchies are studied: the multi-component KP and KdV hierarchies, and the modified KdV hierarchy as their reduction. In particular, the action of additional symmetries on the Grassmannian is found, as well as Virasoro constraints on the $τ$-functions. The matrix string equations are known to be involved in some matrix models.

Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification

Non-invertible symmetries have recently been understood to provide interesting contraints on RG flows of QFTs. In this work, we show how non-invertible symmetries can also be used to generate entirely new RG flows, by means of so-called "non-invertible twisted compactification". We illustrate the idea in the example of twisted compactifications of 4d $\mathcal{N}=4$ super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of non-invertible symmetries descending from Montonen-Olive duality transformations of 4d $\mathcal{N}=4$ SYM, we show that twisted compactification by non-invert…

Loop Algebra Symmetries and Commuting Flows for the Kadomtsev-Petviashvili Hierarchy

The relation between the $\widehat\gl(\infty)$ symmetry of the Kadomtsev-Petviashvili hierarchy and the Kac-Moody-Virasoro Lie point symmetries of the individual equations is established. The Lie point symmetries are shown to be the only local ones.

UV/IR symmetries of the $S$-matrix and RG flow

The low energy $S$-matrix which describes non-relativistic scattering arising from finite-range forces has UV/IR symmetries that are hidden in the corresponding effective field theory (EFT) action. It is shown that the $S$-matrix symmetries are manifest as geometric symmetries of the RG flow of coupling constants in the EFT action in both three and two spatial dimensions. An example is given demonstrating that UV/IR symmetry breaking in the $S$-matrix implies strong constraints on the RG flow of the coefficients of the corresponding symmetry-breaking operators in the EFT.

Discrete Symmetries and S Matrix of the XXZ Chain

We formulate the notion of parity for the periodic XXZ spin chain within the Quantum Inverse Scattering Method. We also propose an expression for the eigenvalues of the charge conjugation operator. We use these discrete symmetries to help classify low-lying S^z=0 states in the critical regime, and we give a direct computation of the S matrix.

Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain

We formulate the notion of parity for the periodic XXZ spin chain within the Quantum Inverse Scattering Method. We also propose an expression for the eigenvalues of the charge conjugation operator. We use these discrete symmetries to help classify low-lying S^z=0 states in the critical regime, and we give a direct computation of the S matrix.

Symmetries of Large N Matrix Models for Closed Strings

We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known results of solvable spin chain systems.

由$\n\b\bZ_2^n$-阶化李超代数生成的$S$-矩阵的新可能对称性

Novel possible symmetries of $S$-matrix generated by $\mathbb{Z}_2^n$-graded Lie superalgebras

本研究提出$\n\b\bZ_2^n$-阶化李（超）代数可作为$S$-矩阵的新型对称生成元，证明其超对称代数扩张及内对称性形式，是两大不可行定理的自然推广。

通过 Matrix Product Operators 实现体积变化对称性

Volume Changing Symmetries by Matrix Product Operators

本文研究了具有改变自旋链长度对称性的自旋链模型，提出利用 Matrix Product Operator 的推广构造此类体积变化对称性，并通过折叠 XXZ 模型等实例证明该对称性与可积性无关。

Determination of quantum symmetries for higher ADE systems from the modular T matrix

We show that the Ocneanu algebra of quantum symmetries, for an ADE diagram (or for higher Coxeter-Dynkin systems, like the Di Francesco - Zuber system) is, in most cases, deduced from the structure of the modular T matrix in the A series. We recover in this way the (known) quantum symmetries of su(2) diagrams and illustrate our method by studying those associated with the three genuine exceptional diagrams of type su(3), namely E5, E9 and E21. This also provides the shortest way to the determination of twisted partition functions in boundary conformal field theory with defect lines.

S矩阵自举与非可逆对称性

S-Matrix Bootstrap and Non-Invertible Symmetries

该研究首次开展(1+1)维非可逆对称理论的S矩阵自举分析，结合幺正性等约束识别可积理论，并拓展交叉规则，凸显SymTFT在散射振幅分析中的作用。

Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems

The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how matrix product states and projected entangled pair states describe many-body wavefunctions in terms of local tensors. These tensors express how the entanglement is routed, act as a novel type of non-local order parameter, and we describe how their symmetries are reflections of the global entanglement patterns in the full system. We will discuss how t…