4 research outputs found
One-Loop QCD Spin Chain and its Spectrum
We study the renormalization of gauge invariant operators in large Nc QCD. We
compute the complete matrix of anomalous dimensions to leading order in the 't
Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the
Hamiltonian of a generalized spin chain we find a large integrable sector
consisting of purely gluonic operators constructed with self-dual field
strengths and an arbitrary number of derivatives. This sector contains the true
ground state of the spin chain and all the gapless excitations above it. The
ground state is essentially the anti-ferromagnetic ground state of a XXX1 spin
chain and the excitations carry either a chiral spin quantum number with
relativistic dispersion relation or an anti-chiral one with non-relativistic
dispersion relation.Comment: 54 pages, v2: minor changes, references adde
Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
We present an "algebraic treatment" of the analytical Bethe Ansatz. For this
purpose, we introduce abstract monodromy and transfer matrices which provide an
algebraic framework for the analytical Bethe Ansatz. It allows us to deal with
a generic gl(n)-spin chain possessing on each site an arbitrary
gl(n)-representation. For open spin chains, we use the classification of the
reflection matrices to treat all the diagonal boundary cases. As a result, we
obtain the Bethe equations in their full generality for closed and open spin
chains. The classifications of finite dimensional irreducible representations
for the Yangian (closed spin chains) and for the reflection algebras (open spin
chains) are directly linked to the calculation of the transfer matrix
eigenvalues. As examples, we recover the usual closed and open spin chains, we
treat the alternating spin chains and the closed spin chain with impurity