Browsing by Author "Mathematics and Theoretical Physics"

Now showing items 1-20 of 119

    • Affine Gaudin models and hypergeometric functions on affine opers 

      Lacroix, Sylvain; Vicedo, Benoit; Young, Charles A. S. (2019-07-09)
      We conjecture that quantum Gaudin models in affine types admit families of higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are given by functions on a space of meromorphic opers ...

    • Affine opers and conformal affine Toda 

      Young, Charles A. S. (2021-12-01)
      Abstract: For g a Kac–Moody algebra of affine type, we show that there is an Aut O ‐equivariant identification between Fun Op g ( D ) , the algebra of functions on the space of g ‐opers on the disc, and W ⊂ π 0 , the ...

    • Affine q-deformed symmetry and the classical Yang-Baxter σ-model 

      Vicedo, Benoit; Delduc, Francois; Magro, Marc; Kameyama, Takashi (2017-03-23)
      The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank(G) × G. It is known that there exist non-local conserved charges ...

    • Algebraic Bethe ansatz for spinor R-matrices 

      Regelskis, Vidas (2022-02-17)
      We present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector Rmatrices. These R-matrices are then used to construct transfer matrices for Uq2(so2n+1)- and Uq(so2n+2)-symmetric closed spin chains. Their ...

    • Amplituhedra, and Beyond 

      Ferro, Livia; Lukowski, Tomasz (2020-12-29)
      This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. ...

    • Amplituhedron meets Jeffrey-Kirwan Residue 

      Ferro, Livia; Lukowski, Tomasz; Parisi, Matteo (2018-12-28)
      The tree amplituhedra A^(m)_n,k are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for m=4 as a geometric construction encoding tree-level scattering amplitudes in planar N=4 super ...

    • An Analog of the Feigin-Frenkel homomorphism for double loop algebras 

      Young, Charles (2021-12-15)
      We prove the existence of a homomorphism of vertex algebras, from the vacuum Verma module over the loop algebra of an untwisted affine algebra, whose construction is analogous to that of the Feigin-Frenkel homomorphism ...

    • Asymptotic Bethe equations for open boundaries in planar AdS/CFT 

      Young, Charles A. S.; Correa, Diego (2010)
      We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries scattering theory describing the excitations of a free open string propagating in $AdS_5\times S^5$, carrying large angular momentum $J=J_{56}$, ...

    • Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones 

      Elliott, L.; Jonusas, Julius; Mitchell, James D.; Morayne, Michal; Mesyan, Zak; Peresse, Yann (2023-08-22)
      In this paper we explore the extent to which the algebraic structure of a monoid M determines the topologies on M that are compatible withits multiplication. Specifically we study the notions of automatic continuity;minimal ...

    • The Bergman-Shelah Preorder on Transformation Semigroups 

      Mesyan, Zak; Mitchell, James D.; Morayne, Michal; Peresse, Yann (2012-11-01)
      Let $\nat^\nat$ be the semigroup of all mappings on the natural numbers $\nat$, and let $U$ and $V$ be subsets of $\nat^\nat$. We write $U\preccurlyeq V$ if there exists a countable subset $C$ of $\nat^\nat$ such that $U$ ...

    • Bethe Equations for a g_2 Model 

      Crampe, N.; Young, Charles A. S. (2005-12-06)
      We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. ...

    • Bruck-Reilly extensions of direct products of monoids and completely (0-)simple semigroups 

      Carvalho, Catarina (2009-08)

    • Caterpillar duality for constraint satisfaction problems 

      Carvalho, Catarina; Dalmau, Víctor; Krokhin, Andrei (Institute of Electrical and Electronics Engineers (IEEE), 2008)

    • CD(4) has bounded width 

      Carvalho, Catarina; Dalmau, Víctor; Marković, Petar; Maróti, Miklós (2009)
      We prove that the constraint languages invariant under a short sequence of J\'onsson terms (containing at most three non-trivial ternary terms) are tractable by showing that they have bounded width. This improves the ...

    • Chains of subsemigroups 

      Cameron, Peter J.; Gadouleau, Maximilien; Mitchell, James D.; Peresse, Yann (2017-06)
      We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations ...

    • Classically integrable boundary conditions for symmetric-space sigma models 

      Mackay, N.; Young, Charles A. S. (2004-05)
      We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an involution $\sigma$ of $G$. The Poisson brackets and the classical local ...

    • Cluster Adjacency for m=2 Yangian Invariants 

      Lukowski, Tomasz; Parisi, Matteo; Spradlin, Marcus; Volovich, Anastasia (2019-10-14)
      We classify the rational Yangian invariants of the $m=2$ toy model of $\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an ...

    • Colour-kinematics duality, double copy, and homotopy algebras 

      Borsten, Leron; Kim, Hyungrok; Jurčo, Branislav; Macrelli, Tommaso; Saemann, Christian; Wolf, Martin (2022-07-06)
      Colour-kinematics duality is a remarkable property of Yang-Mills theory. Its validity implies a relation between gauge theory and gravity scattering amplitudes, known as double copy. Albeit fully established at the tree ...

    • A comparison of methods for traversing regions of non-convexity in optimization problems 

      Bartholomew-Biggs, Michael; Beddiaf, Salah; Christianson, Bruce (2019-11-13)
      This paper considers the well-known problem of dealing with non-convexity during the minimization of a non-linear function f(x) by Newton-like methods. The proposal made here involves a curvilinear search along an approximation ...

    • The complexity of quantified constraints using the algebraic formulation 

      Carvalho, Catarina; Martin, Barnaby; Zhuk, Dmitriy (2017-11-07)