School of Mathematics
http://hdl.handle.net/2262/1
School of MathematicsFri, 21 Oct 2016 16:33:53 GMT2016-10-21T16:33:53ZDiscrete exterior calculus with applications to flows and spinors
http://hdl.handle.net/2262/76932
Discrete exterior calculus with applications to flows and spinors
De Beaucé, Vivien
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/2262/769322005-01-01T00:00:00ZQuantum spectral curve as a tool for a perturbative quantum field theory
http://hdl.handle.net/2262/76887
Quantum spectral curve as a tool for a perturbative quantum field theory
VOLIN, DMYTRO
An iterative procedure perturbatively solving the quantum spectral curve of planar N=4N=4 SYM for any operator in the slsl(2) sector is presented. A Mathematica notebook executing this procedure is enclosed. The obtained results include 10-loop computations of the conformal dimensions of more than ten different operators.
We prove that the conformal dimensions are always expressed, at any loop order, in terms of multiple zeta-values with coefficients from an algebraic number field determined by the one-loop Baxter equation. We observe that all the perturbative results that were computed explicitly are given in terms of a smaller algebra: single-valued multiple zeta-values times the algebraic numbers.
PUBLISHED
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2262/768872015-01-01T00:00:00ZSpectroscopy of doubly charmed baryons from lattice QCD
http://hdl.handle.net/2262/74473
Spectroscopy of doubly charmed baryons from lattice QCD
FERREIRA, MAURO
We present the ground and excited state spectra of doubly charmed baryons from lattice QCD with dynamical quark fields. Calculations are performed on anisotropic lattices of size 163×128, with inverse spacing in temporal direction at-1=5.67(4)GeV and with a pion mass of about 390 MeV. A large set of baryonic operators that respect the symmetries of the lattice yet which retain a memory of their continuum analogues are used. These operators transform as irreducible representations of SU(3)F symmetry for flavor, SU(4) symmetry for Dirac spins of quarks and O(3) for spatial symmetry. The distillation method is utilized to generate baryon correlation functions which are analyzed using the variational fitting method to extract excited states. The lattice spectra obtained have baryonic states with well-defined total spins up to 7/2 and the pattern of low-lying states does not support the diquark picture for doubly charmed baryons. On the contrary the calculated spectra are remarkably similar to the expectations from models with an SU(6)×O(3) symmetry. Various spin-dependent energy splittings between the extracted states are also evaluated.
PUBLISHED
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2262/744732015-01-01T00:00:00ZCacti and filtered distributive laws
http://hdl.handle.net/2262/73949
Cacti and filtered distributive laws
DOTSENKO, VLADIMIR
Motivated by the second author’s construction of a classifying space for the group of
pure symmetric automorphisms of a free product, we introduce and study a family of
topological operads, the operads of based cacti, defined for every pointed simplicial
set
.
Y
;
p
/
. These operads also admit linear versions, which are defined for every
augmented graded cocommutative coalgebra
C
. We show that the homology of the
topological operad of based
Y
–cacti is the linear operad of based
H
.
Y
/
–cacti. In
addition, we show that for every coalgebra
C
the operad of based
C
–cacti is Koszul.
To prove the latter result, we use the criterion of Koszulness for operads due to the
first author, utilising the notion of a filtered distributive law between two quadratic
operads. We also present a new proof of that criterion, which works over a ground
field of arbitrary characteristic
PUBLISHED
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2262/739492015-01-01T00:00:00Z