Kurt Hinterbichler
Massive fields on (anti) de Sitter space realize extended shift symmetries at particular values of their masses. We find these symmetries for all bosonic p-forms and mixed symmetry fields, in arbitrary spacetime dimension. These shift symmetric fields correspond to the missing longitudinal modes of mixed symmetry partially massless fields where the top row of the Young tableau is activated.
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Chiral shift symmetries as an infinite tower of subleading super-shift symmetries
本文研究二维无质量自由玻色子的手性平移对称性，指出其在双零坐标中由两个单变量函数参数化，并在BMS型坐标中表现为无穷阶次超平移对称性塔。
Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space-time derivatives of the fields, we investigate the consistent cross-couplings between two collections of tensor fields with the mixed symmetries of the type (3,1) and (2,2). The computations are done with the help of the deformation theory based on a cohomological approach in the context of the antifield-BRST formalism. Our results can be synthesized in: 1. there appear consistent cross-couplings be…
Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete zero-form global symmetries, and possibly a one-form symmetry, in 3d $\mathcal{N} \geq 3$ gauge theories using the superconformal index. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, such as the $\mathrm{U}(1)_k$ gauge theory with hypermultiplets of diverse charges, the $T(\mathrm{S…
Mixed Symmetries of SPT Phases
本文主张在SPT相的对称性描述中纳入拓扑扭曲场，从而预测对其部分或全部对称性进行规范所得的结果。
Mixed-helicity bracket of celestial symmetries
本文从协变相空间视角分析了引力和杨-米尔斯理论中高自旋电荷的混合螺旋度括号结构，展示了通过引入阴影电荷概念可得到闭合代数，并在引力中构建了双质量扩展的BMS代数，在麦克斯韦理论中通过引入磁电荷恢复了非零电磁中心电荷。
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first class constraints. In the latter approach such local symmetries are reflected in the existence of so called gauge identities. The connection between the two becomes apparent, if one works with a first order Lagrangean formulation. We thereby confirm Dirac's conjecture. Our analysis applies to arbitrary constrained systems with first and second class constraints…
Conformal Killing Tensors, Noether Currents and Higher-Spin Shift Symmetries in (A)dS Space
研究了(A)dS空间中高自旋场的位移对称性与conformal Killing张量的关系，揭示了守恒流的等价性及非冗余结构。
SymTFT Approach for Mixed States with Non-Invertible Symmetries
该研究针对具有非可逆对称性的混合态相问题，提出基于SymTFT方法的通用框架，通过混合态纯化与双倍希尔伯特空间分类，覆盖群及非可逆对称性，在1+1维验证并结合格点模型分析，支持强弱对称组合研究。
Generalized symmetry-protected topological phases in mixed states from gauging dualities
本文研究混合态中广义对称性保护拓扑相的分类，通过 gauge 对应将广义对称性与普通群对称性联系起来，利用字符串序参数和保护边缘模式描述非可逆和偶极对称性的ASPT相。
Intrinsic mixed-state SPT from modulated symmetries and hierarchical structure of anomaly
本研究在开放量子系统中提出一类具有调制对称性的内禀混合态对称性保护拓扑相（mSPT），通过可解耦合线模型构建其密度矩阵微观形式，对比纯态与混合态的边界反常层级，并指出其边界反常特征可通过带电可观测量的Renyi-N关联函数探测。
Generalised symmetries in linear gravity
本文研究线性引力中的广义对称性，发现引力子与对偶引力子的平移对称性对应中心扩展代数，并存在混合't Hooft反常，二者可视为南部-戈德斯通模式。
Mixed Anomalies of Magnetic Symmetries
本文通过目标空间Whitehead塔中的higher group结构，解决了σ-模型与规范理论中电磁对称性混合't Hooft反常的起源与分类问题，并揭示了映射类群带来的新特征及non-invertible情形。
Shift Symmetries and AdS/CFT
本文探讨了AdS空间中大质量场的shift对称性如何通过边界CFT的两点函数实现，发现在alternate量子化中表现为规范对称性，在标准量子化中作用于源并产生积分约束形式的Ward恒等式。
The fate of shift-symmetries in effective string models is considered beyond tree-level. Such symmetries have been proposed in the past as a way to maintain a hierarchically small Higgs mass and also play a role in schemes of cosmological relaxation. It is argued that on general grounds one expects shift-symmetries to be restored in the limit of certain asymmetric compactifications, to all orders in perturbation theory. This behaviour is verified by explicit computation of the Kaehler potential to one-loop order.
Shift Symmetries in (Anti) de Sitter Space
本文研究了反德西特和德西特空间中所有整数自旋场的扩展位移对称性，扩展了平直空间中无质量标量场的位移对称性、鬼魅对称性和特殊鬼魅对称性，讨论了其在部分无质量极限下的应用。
On mixed 't Hooft anomalies of emergent symmetries
研究紫外理论在红外区域出现含混合 't Hooft 反常的涌现对称性时的动力学约束，以二维规范线性西格玛模型等为例，建立拓扑量子场论联系并提出量子上同调对应关系。
In this paper, we compute the higher derivative amplitudes arising from shift symmetric-invariant actions for both the non-linear sigma model and the special galileon symmetries, and provide explicit expressions for their Lagrangians. We find that, beyond leading order, the equivalence between shift symmetries, enhanced single soft limits, and compatibility with the double copy procedure breaks down. In particular, we have shown that the most general even-point amplitudes of a colored-scalar satisfying the Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations are compatible with the no…
Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
本文研究 d=2、3 量子自旋模型中 higher-form 有限 Abelian 对称性的规范变换，揭示混合反常、对称分数化及有隙相/拓扑序对偶，并指出自对偶模型可涌现不可逆对称性。
Higher-form anomaly and long-range entanglement of mixed states
本文利用随机局域信道定义混合态长程纠缠等价类，通过强对称性拉回证明高形式反常蕴含长程纠缠，并以toric code噪声模型验证。
We consider scalar field theories invariant under extended shift symmetries consisting of higher order polynomials in the spacetime coordinates. These generalize ordinary shift symmetries and the linear shift symmetries of the galileons. We find Wess-Zumino Lagrangians which transform up to total derivatives under these symmetries, and which possess fewer derivatives per field and lower order equations of motion than the strictly invariant terms. In the non-relativistic context, where the extended shifts are purely spatial, these theories may describe multi-critical Goldstone bosons. In the re…
(-1)-Form Symmetries and Anomaly Shifting from SymTFT
本文研究了(-1)-形式对称性在SymTFT中的表现，揭示了其通过更高规范化构造的本征缺陷生成元，并展示了其能偏移't Hooft异常的能力。
Tensor global symmetries and the Stueckelberg mechanism for tensor fields
本研究探究张量整体对称性，构建线性化层面混合对称张量场的Stueckelberg机制，分析三类有质量场的对应场集合与守恒流，并通过非最小耦合发现线性化引力的't Hooft反常。
Mixed Gauge-Global Symmetries, Elliptic Modes, and Black Hole Thermodynamics in Hořava-Lifshitz Gravity
针对Hořava-Lifshitz引力中第一定律失效问题，本文揭示了混合规范-全局对称性及其相关荷的动力学机制，解决了渐近AdS解的热力学矛盾，并阐明了该对称性如何规避量子引力中仅含局部规范场的全息论证。
We investigate the four-derivative free Weyl action for two-column mixed-symmetry field that makes use of maximal gauge symmetries. In flat space, the action can be uniquely determined from gauge and Weyl (trace shift) symmetry requirements. We show that there is a smooth and unique deformation of the flat action to (A)dS which keeps the same amount of gauge symmetries. This action admits a factorization into two distinct two-derivative actions having gauge parameters of different Young diagrams. Hence, this factorization pattern naturally extends that of the Weyl actions of symmetric higher s…
We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We ge…
We study confinement in 4d $\mathcal{N}=1$ $SU(N)$ Super-Yang Mills (SYM) from a holographic point of view, focusing on the 1-form symmetry and its relation to chiral symmetry breaking. In the 5d supergravity dual, obtained by truncation of the Klebanov-Strassler solution, we identify the topological couplings that determine the 1-form symmetry and its 't Hooft anomalies. One such coupling is a mixed 0-form/1-form symmetry anomaly closely related to chiral symmetry breaking in gapped confining vacua. From the dual gravity description we also identify the infra-red (IR) 4d topological field the…
Gravity Decoupling and Axionic Shift Symmetries
本文分析II型Calabi-Yau紧化中引力退耦极限下近似轴子平移对称性的作用，通过轴子弦张力约束Kähler势梯度，并证明这些张力梯度矢量在模空间中分裂为相互正交的子集，其中一部分从引力退耦。
We consider a BMS-type symmetry action on isolated horizons in asymptotically flat spacetimes. From the viewpoint of the non-relativistic field theory on a horizon membrane, supertranslations shift the field theory spatial momentum. The latter is related by a Ward identity to the particle number symmetry current and is spontaneously broken. The corresponding Goldstone boson shifts the horizon angular momentum and can be detected quantum mechanically. Similarly, area preserving superrotations are spontaneously broken on the horizon membrane and we identify the corresponding gapless modes. In as…
Non-invertible symmetries and mixed anomalies from conserved current construction in (3+1)D twisted $BF$ topological quantum field theories
本研究通过守恒流构造方法，探讨了(3+1)维扭曲BF拓扑量子场论中非可逆对称性与混合异常的生成机制，揭示了非可逆对称性的融合代数及异常诊断方法。
Gauging staggered fermion shift symmetries
本研究提出通过让关联的Z₂整体参数局域化来部分规范交错费米子平移对称性的策略，需引入Z₂高形式晶格规范场以保持作用量不变，且该方法可推广至约化交错费米子体系。
Fermionic Shift Symmetries in (Anti) de Sitter Space
本研究分类了AdS与dS空间中费米子场在特定质量下的扩展移位对称性，探究了其作为部分无质量费米子解耦纵向模的起源，并以AdS₄上的Akulov–Volkov理论为例分析了相关李超代数，排除了超对称特殊伽利略子的存在。
We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d $\mathcal{N}=1$ SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d $\mathcal{N}=1$ SYM theory, w…
Covariant Lagrangian formulation for free bosonic massless fields of arbitrary mixed-symmetry type in (A)dS(d) space-time is presented. The analysis is based on the frame-like formulation of higher-spin field dynamics [1] with higher-spin fields described as p-forms taking values in appropriate modules of the (A)dS(d). The problem of finding free field action is reduced to the analysis of an appropriate differential complex, with the derivation Q associated with the variation of the action. The constructed action exhibits additional gauge symmetries in the flat limit in agreement with the gene…
Symmetries and Anomalies of Hamiltonian Staggered Fermions
本文回顾哈密顿交错费米子的平移和时间反演对称性，构造有限格点上的对称性算符，证明奇数倍位移与时间反演反对易并关联轴变换，由此论证格点't Hooft反常，并构造守恒量子化荷揭示更多反常。
Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
本文提出了一种扩展的数学框架，用于分类具有混合空间对称性的费米子相，并证明了费米子晶格等价原理。
New horizon symmetries, hydrodynamics, and quantum chaos
本文推广视界对称性表述以纳入可移动视界的微分同胚，在 AdS/CFT 中将其识别为边界涌现低能规范对称性，并发现扩展平移对称性的新类别，同时联系 OTOC 与极点跳过。
Gauging generalised symmetries in linear gravity
本文研究了Minkowski时空中自由自旋-2场的广义对称性，证明部分对称性可解释为引力子特定平移对称性的Noether流，提出系统方法规范1-形式对称性，并揭示由引力对偶性相关的1-形式与$(d-3)$-形式对称性对同时规范化时存在混合't Hooft反常。
Dilaton shifts, probability measures, and decomposition
本文研究二维量子场论分解中的伸缩子位移，构造其一般公式并揭示其与不可逆量子对称性及系综的联系。
Building far-from-equilibrium effective field theories using shift symmetries
针对量子场论中不同耦合强度下非流体动力学瞬态激发行为缺乏统一解释的问题，基于平移对称性构建远平衡流体动力学有效作用量，统一解释已知激发行为，构建可在强弱耦合间插值的混合模型并结合QCD跑动耦合研究核碰撞热化相关模型性质。
We study the global symmetries of naive lattices Dirac operators in QCD-like theories in any dimension larger than two. In particular we investigate how the chosen number of lattice sites in each direction affects the global symmetries of the Dirac operator. These symmetries are important since they do not only determine the infra-red spectrum of the Dirac operator but also the symmetry breaking pattern and, thus, the lightest pseudo-scalar mesons. We perform the symmetry analysis and discuss the possible zero modes and the degree of degeneracy of the lattice Dirac operators. Moreover we expli…
Intrinsic NISPT Phases, igNISPT Phases, and Mixed Anomalies of Non-Invertible Symmetries
本文针对非可逆对称性保护拓扑相的分类与构建问题，通过带混合反常的融合范畴对称部分SSB相的离散规范操作，构建了内禀NISPT相、igNISPT相，给出格点实现并推广至(3+1)维。
We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength $f^{(2)}$, naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current $J^{(2)} \sim * \text{Tr} \left( f^{(2)} \wedge f^{(2)}\right)$. We show that suitable mixed anomalies involving the gauge field $f^{(2)}$ and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tenso…
There are several instances where quantum anomalies of continuous and discrete classical symmetries play an important role in fundamental physics. Examples come from chiral anomalies in the Standard Model of fundamental interactions and gravitational anomalies in string theories. Their generic origin is the fact that classical symmetries may not preserve the domains of quantum operators like the Hamiltonian. In this work, we show by simple examples that anomalous symmetries can often be implemented at the expense of working with mixed states having non-zero entropies. In particular there is th…
We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift $k \to k+\cv$ of the bare Chern-Simons parameter $k$ in conncection with the Landau supersymmetry. Finally, to convince ourselves that the s…
The symmetries and dynamics of simple chiral $SU(N)$ gauge theories, with matter Weyl fermions in a two-index symmetric tensor and $N+4$ anti-fundamental representations, are examined, by taking advantage of the recent developments involving the ideas of generalized symmetries, gauging of discrete center 1-form symmetries and mixed 't Hooft anomalies. This class of models are particularly interesting because the conventional 't Hooft anomaly matching constraints allow a chirally symmetric confining vacuum, with no condensates breaking the $U(1) \times SU(N+4)$ flavor symmetry, and with certain…
Mixed-state Phases from Higher-order SSPTs with Kramers-Wannier Symmetry
本研究探讨了高阶子系统SPT相通过消去bulk自由度后获得的混合态相，发现其同时包含对称保护拓扑序和强到弱对称破缺特性。
We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field theories with such 2-group symmetries. The approach taken in 6d is applicable more generally, with minor modifications to include dimension specific operators (such as instantons in 5d and monopoles in 3d), and we provide a discussion of the dimension-independent aspects of the analysis. We include an ancillary mathematica code for computing 2-group symmetries, on…
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrela…
The unfolded formulation for arbitrary massless mixed-symmetry bosonic and fermionic fields in Minkowski space is constructed. The unfolded form is proved to be uniquely determined by the requirement that all gauge symmetries are manifest. The unfolded equations have the form of a covariant constancy condition. The gauge fields and gauge parameters are differential forms with values in certain irreducible Lorentz tensors. The unfolded equations for bosons determine completely those for fermions. The proposed unfolded formulation also contains dual formulations for massless mixed-symmetry field…
Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems
本文研究格点模型中型IV 't Hooft异常的涌现对称性，揭示了2群、非可逆及更高融合范畴对称性的出现，并探讨其在LSM系统中的应用。
Shift symmetries and duality web in gauge theories
本文用广义 Noether 方案提取平移对称理论的流与守恒律，并通过矢量及高阶张量规范场耦合建立对偶映射和电磁定律对应。
We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized gravity, and then the ($γ$-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.
Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement
本研究证明高形式对称性反常会强制产生内禀长程纠缠，并利用此特性诊断混合态拓扑序，发现了一种破坏远程可探测性的新内禀混合态拓扑序。
Starting from a nonlinear isospinor-spinor field equation, generalized three-particle Bargmann-Wigner equations are derived. In the strong-coupling limit, a special class of spin 1/2 bound-states are calculated. These solutions which are antisymmetric with respect to all indices, have mixed symmetries in isospin-superspin space and in spin orbit space. As a consequence of this mixed symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these solution manifolds are interpreted as the three generations of leptons and quarks. This interpretation will be justified in a forthcomi…
We investigate a large class of infinitesimal, but fully nonlinear in the field, transformations of the Galileon and search for extended symmetries. The transformations involve powers of the coordinates $x$ and the field $π$ up to any finite order $N$. Up to quadratic order the structure of these symmetry transformations is the unique generalisation of both the infinitesimal version of the standard Galileon shift symmetry as well as a recently discovered infinitesimal extension of this symmetry. The only higher-order extensions of this symmetry we recover are (`Galileon dual' versions of) symm…
Symmetries, anomalies, and dualities of two-dimensional Non-Linear Sigma Models
本文研究了二维非线性σ模型的对称性结构，探讨了Wess-Zumino项对连续和离散对称性的影响，并分析了非可逆对称性与自对偶性之间的关系。
Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations
研究 5 维 $\mathcal{N}=1$ 理论的广义全局对称性，通过爆破方程提取相关数据，包括 1 - 形式对称性的立方自反常及混合反常等，结合超共形指标确定的对称性，判断理论是否有 2 - 群对称性或混合 't Hooft 反常，在多种理论中演示并获新结果。
Anomaly and symmetry-charge flow in mixed states
本文研究了混合态中异常与对称性-电荷流的机制，通过代数关系推导出对称性与通量插入算符之间的关系，恢复了异常的普遍性，适用于费米和玻色系统。
We show that the fully covariant equations of motion for the M-theory fivebrane can be interpreted as charge conservation equations. The associated charges induce `shift'-symmetries of the scalar, spinor and gauge-fields of the fivebrane, so allowing an interpretation of all these fields as Goldstone fields. We also find that the fivebrane possesses a new symmetry that is part of the GL(32) automorphism group of the eleven dimensional supersymmetry algebra.
Comments on Global Symmetries and Anomalies of $5d$ SCFTs
本研究探讨五维超对称共形场论的整体对称性，揭示相关形变下红外规范理论的1-形式与瞬子对称性的混合't Hooft反常对味对称群及RG流的约束，辅以三维案例验证，并分析共形不变性与高阶整体对称性的相容性。
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