Superuniversality of Superdiffusion by Enej Ilievski, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

“…This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it “superuniversal.” …”
Get full text

The group structure of dynamical transformations between quantum reference frames by Angel Ballesteros, Flaminia Giacomini, Giulia Gubitosi

“…In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. …”
Get full text

The Algebra and Calculus of Stochastically Perturbed Spacetime with Classical and Quantum Applications by Dragana Pilipović

“…ML spacetime follows the Lie algebra of the Poincare group, now expressed in terms of the two-point functions of the stochastic fields (per Ito’s lemma). …”
Get full text

Four-Dimensional Spin Foam Perturbation Theory by João Faria Martins, Aleksandar Mikovic

“…We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group U_q(g) where g is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners Λ⊗Λ→A, where A is the adjoint representation of g, is 1-dimensional for each irrep Λ. …”
Get full text

Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing by Beem, C, Nair, S

“…The construction of Arakawa (2018) takes as input a choice of simple Lie algebra g, and applies equally well regardless of whether g is simply laced or not. …”

Γ-invariant ideals in Iwasawa algebras by Ardakov, K, Wadsley, S

“…The minimal codimension of these subspaces gives a lower bound on the homological height of I in terms of the action of a certain Lie algebra on G / Gp. If we take Γ to be G acting on itself by conjugation, then Γ-invariant right ideals of k G are precisely the two-sided ideals of k G, and we obtain a non-trivial lower bound on the homological height of a possible non-zero two-sided ideal. …”

<italic>SE</italic>(3) Based LTV-MPC Algorithm for Multi-Obstacle Trajectory Tracking of Fully Driven Spacecraft by Wenbang Wang, Xiaokang Peng, Jia Ai, Cheng Fu, Chaobo Li, Zejian Zhang

“…First, left-invariant principle of Lie group, Lie algebra <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula>, and other differential geometry theories are applied to extend LTV-MPC to <inline-formula> <tex-math notation="LaTeX">$SE(3)$ </tex-math></inline-formula>. …”
Get full text

Four-mode squeezed states: two-field quantum systems and the symplectic group $$\mathrm {Sp}(4,{\mathbb {R}})$$ Sp ( 4 , R ) by Thomas Colas, Julien Grain, Vincent Vennin

“…For this reason, we first present a pedagogical analysis of the symplectic group $$\mathrm {Sp}(4,{\mathbb {R}})$$ Sp ( 4 , R ) and its Lie algebra, from which we construct the four-mode squeezed states and discuss their structure. …”
Get full text

Exact results in a N $$ \mathcal{N} $$ = 2 superconformal gauge theory at strong coupling by M. Beccaria, M. Billò, M. Frau, A. Lerda, A. Pini

“…Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ. …”
Get full text

A bispinor formalism for spinning Witten diagrams by Damon J. Binder, Daniel Z. Freedman, Silviu S. Pufu

“…In our CFT3 formalism, we identify an so $$ \mathfrak{so} $$ (5, 5) Lie algebra of differential operators that includes the basic weight-shifting operators. …”
Get full text

Next-to-MHV Yang-Mills kinematic algebra by Gang Chen, Henrik Johansson, Fei Teng, Tianheng Wang

“…Abstract Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. …”
Get full text

Stability Conditions for Slodowy Slices and Real Variations of Stability by Mirkovic, Ivan, Anno, Irina, Bezrukavnikov, Roman

“…More precisely, let X be the standard resolution of a transversal slice to an adjoint nilpotent orbit of a simple Lie algebra over C. An action of the affine braid group on the derived category D[superscript b] (Coh(X)) and a collection of t-structures on this category permuted by the action have been constructed in [BR] and [BM] respectively. …”
Get full text
Get full text

A bispinor formalism for spinning Witten diagrams by Binder, Damon J., Freedman, Daniel Z., Pufu, Silviu S.

“…In our CFT3 formalism, we identify an so $$ \mathfrak{so} $$ (5, 5) Lie algebra of differential operators that includes the basic weight-shifting operators. …”
Get full text

A quantum check of non-supersymmetric AdS/dCFT by Aleix Gimenez Grau, Charlotte Kristjansen, Matthias Volk, Matthias Wilhelm

“…Supergravity predicts, in a certain double-scaling limit, the value of the one-point functions of chiral primaries of the dual defect version of N = 4 $$ \mathcal{N}=4 $$ SYM theory, where the fluxes translate into SO(3) × SO(3)-symmetric, Lie-algebra-valued vacuum expectation values for all six scalar fields. …”
Get full text

Webs of W-algebras by Tomáš Procházka, Miroslav Rapčák

“…Many well-known vertex operator algebras, such as U(N) k affine Lie algebra, N = 2 $$ \mathcal{N}=2 $$ superconformal algebra, N = 2 $$ \mathcal{N}=2 $$ super- W ∞ $$ {\mathcal{W}}_{\infty } $$ , Bershadsky-Polyakov W 3 2 $$ {\mathcal{W}}_3^{(2)} $$ , cosets and Drinfeld-Sokolov reductions of unitary groups can be obtained as special cases of this construction.…”
Get full text

Modeling of entangled states in qubit clusters by E. Andre, A.N. Tsirulev

“…It turns out that the approach based on the representation of Hamiltonians and unitary transformations in the Pauli basis is the most suitable in this context for two reasons: firstly, the Pauli basis forms the Lie algebra of the corresponding unitary group; secondly, there are only real coefficients in the decompositions of Hamiltonians and state density operators in this basis. …”
Get full text

SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement by Richard Lau, Michael Teper

“…We also compare the glueball spectra of those pairs of SO(N) and SU(N′) theories that possess the same Lie algebra, i.e. SO(3) and SU(2), SO(4) and SU(2)×SU(2), SO(6) and SU(4), and find that for the very lightest glueballs the spectra are consistent within each such pair, as are the string tensions and the couplings. …”
Get full text

Carroll versus Galilei from a brane perspective by Eric Bergshoeff, José Manuel Izquierdo, Luca Romano

“…We show that this formal map extends to the corresponding Lie algebra expansion of the Poincaré algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. …”
Get full text

Peculiarities of beta functions in sigma models by Oleksandr Gamayun, Andrei Losev, Mikhail Shifman

“…In addition to the generic Kähler target spaces we discuss in detail the so-called Lie-algebraic sigma models. In particular, this is the case when the perturbed field G i j ¯ $$ {G}^{i\overline{j}} $$ is a product of the holomorphic and antiholomorphic currents satisfying two-dimensional current algebra.…”
Get full text

Duality and form factors in the thermally deformed two-dimensional tricritical Ising model by Axel Cortés Cubero, Robert M. Konik, Máté Lencsés, Giuseppe Mussardo, Gabor Takács

“…The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases of this model are related by duality. …”
Get full text