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The complexity of quantified constraints: Collapsibility, switchability and the algebraic formulation
Carvalho, Catarina; Madelaine, Florent; Martin, Barnaby; Zhuk, Dmitriy (2023-01-18)Let A be an idempotent algebra on a finite domain. By mediating between results of Chen and Zhuk, we argue that if A satisfies the polynomially generated powers property (PGP) and B is a constraint language invariant under ... -
Computer modelling and visualisation of the structural deformation caused by movement along geological faults
Kane, Stephen; Williams, Graham; Egan, Stuart; Buddin, Tim; Hodgetts, David (1999-04-15)The computer modelling and visualisation of deformation caused by movement along faults has enhanced our understanding of the evolution of fault-related structures in the geological record. In particular, the development ... -
Computing finite semigroups
East, James; Egri-Nagy, Attila; Mitchell, James D.; Peresse, Yann (2019-05-01)Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples ... -
Conformal Sigma-Models on Supercoset Targets
Kagan, David; Young, Charles A. S. (2005-12-20)We investigate the quantum behaviour of sigma models on coset superspaces G/H defined by Z_{2n} gradings of G. We find that, whenever G has vanishing Killing form, there is a choice of WZ term which renders the model quantum ... -
Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
Young, Charles A. S.; Zegers, R. (2008-03-18)We consider the exchange of identical scalar particles in theories with kappa-deformed Poincare symmetry. We argue that, at least in 1+1 dimensions, the symmetric group S_N can be realized on the space of N-particle states ... -
Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
Young, Charles A. S.; Zegers, R. (2007-11-14)To speak about identical particles - bosons or fermions - in quantum field theories with kappa-deformed Poincare symmetry, one must have a kappa-covariant notion of particle exchange. This means constructing intertwiners ... -
CSP duality and trees of bounded pathwidth
Carvalho, Catarina; Dalmau, Víctor; Krokhin, Andrei (2010)We study non-uniform constraint satisfaction problems definable in monadic Datalog stratified by the use of non-linearity. We show how such problems can be described in terms of homomorphism dualities involving trees of ... -
Cubic hypergeometric integrals of motion in affine Gaudin models
Lacroix, Sylvain; Vicedo, Benoit; Young, Charles A. S. (2020-05-22)We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute ... -
Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras
Varchenko, Alexander; Young, Charles A. S. (2017-09-25)Recently a new class of quantum integrable models, the cyclotomic Gaudin models, were described in arXiv:1409.6937, arXiv:1410.7664. Motivated by these, we identify a class of affine hyperplane arrangements that we call ... -
Cyclotomic Gaudin models with irregular singularities
Vicedo, Benoit; Young, Charles (2017-11-01)Generalizing the construction of the cyclotomic Gaudin algebra from arXiv:1409.6937, we define the universal cyclotomic Gaudin algebra. It is a cyclotomic generalization of the Gaudin models with irregular singularities ... -
Deformation Quasi-Hopf Algebras of Non-semisimple Type from Cochain Twists
Young, Charles A. S.; Zegers, Robin (2010)One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist ... -
Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
Young, Charles A. S.; Zegers, R. (2011)Let Uq(ghat) be the quantum affine algebra associated to a simply-laced simple Lie algebra g. We examine the relationship between Dorey's rule, which is a geometrical statement about Coxeter orbits of g-weights, and the ... -
Double-copying self-dual Yang-Mills theory to self-dual gravity on twistor space
Borsten, Leron; Jurčo, Branislav; Kim, Hyungrok; Macrelli, Tommaso; Saemann, Christian; Wolf, Martin (2023-11-24)We construct a simple Lorentz-invariant action for maximally supersymmetric self-dual Yang-Mills theory that manifests colour-kinematics duality. We also show that this action double-copies to a known action for maximally ... -
Equivalences between three presentations of orthogonal and symplectic Yangians
Guay, Nicolas; Regelskis, Vidas; Wendlandt, Curtis (2019-02-01)We prove the equivalence of two presentations of the Yangian Y(g) of a simple Lie algebra g, and we also show the equivalence with a third presentation when g is either an orthogonal or a symplectic Lie algebra. As an ... -
Expanding the Bethe/Gauge Dictionary
Bullimore, Mathew; Kim, Hee-Cheol; Lukowski, Tomasz (2017-11-09)We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe ... -
Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra
Ashmore, Anthony; de la Ossa, Xenia; Minasian, Ruben; Strickland-Constable, Charles; Svanes, Eirik Eik (2018-10-29)We consider finite deformations of the Hull-Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric ... -
Finite generation of P-semigroups with almost G-invariant idempotents
Carvalho, Catarina (World Scientific Publishing, 2007-06) -
Finite presentability of Bruck-Reilly extensions of Clifford monoids
Carvalho, Catarina (2007-10)Let M be a Clifford monoid and let θ be an endomorphism of M. We prove that if the Bruck–Reilly extension BR(M, θ) is finitely presented then M is finitely generated. This allows us to derive necessary and sufficient ... -
Finite size corrections for open strings/open chains in planar AdS/CFT
Correa, Diego; Young, Charles A. S. (2009-05-11)We identify the leading finite-size (Luscher-type) correction to the energy of open strings ending on maximal giant gravitons. In particular we obtain the leading finite size correction at weak 't Hooft coupling and in the ... -
A finitely presented monoid with a non-finitely generated group of units
Carvalho, Catarina; Ruskuc, Nik (2007-08)We exhibit an example of a monoid defined by finitely many generators and defining relations, the group of units of which is not finitely generated