10,096 research outputs found
On difference matrices of coset type
AbstractA (u,k;λ)-difference matrix H over a group U is said to be of coset type with respect to one of its rows, say w, whose entries are not equal, if it has the property that rw is also a row of H for any row r of H. In this article we study the structural property of such matrices with u(<k) a prime and show that u|λ and, moreover, H contains u (u,k/u;λ/u)-difference submatrices and is equivalent to a special kind of extension using them. Conversely, we also show that any set of u (u,k′;λ′)-difference matrices over U yields a (u,uk′;uλ′)-difference matrix of coset type over U
Yang-Baxter sigma models and Lax pairs arising from -Poincar\'e -matrices
We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes
arising from classical -matrices associated with -deformations of
the Poincar\'e algebra. These classical -Poincar\'e -matrices
describe three kinds of deformations: 1) the standard deformation, 2) the
tachyonic deformation, and 3) the light-cone deformation. For each deformation,
the metric and two-form -field are computed from the associated -matrix.
The first two deformations, related to the modified classical Yang-Baxter
equation, lead to T-duals of dS and AdS\,, respectively. The third
deformation, associated with the homogeneous classical Yang-Baxter equation,
leads to a time-dependent pp-wave background. Finally, we construct a Lax pair
for the generalized -Poincar\'e -matrix that unifies the three kinds
of deformations mentioned above as special cases.Comment: 31 pages, v2: some clarifications and references added, published
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Strings on Semisymmetric Superspaces
Several string backgrounds which arise in the AdS/CFT correspondence are
described by integrable sigma-models. Their target space is always a Z(4)
supercoset (a semi-symmetric superspace). Here we list all semi-symmetric
cosets which have zero beta function and central charge c<=26 at one loop in
perturbation theory.Comment: 25 pages, 1 figur
Deformations of as Yang-Baxter sigma models
We consider a family of deformations of T^{1,1} in the Yang-Baxter sigma
model approach. We first discuss a supercoset description of T^{1,1}, which
makes manifest the full symmetry of the space and leads to the standard
Sasaki-Einstein metric. Next, we consider three-parameter deformations of
T^{1,1} by using classical r-matrices satisfying the classical Yang-Baxter
equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the
ones obtained via TsT transformations, and contain the Lunin-Maldacena
background as a special case. It is worth noting that for AdS_5 x T^{1,1},
classical integrability for the full sector has been argued to be lost. Hence
our result indicates that the Yang-Baxter sigma model approach is applicable
even for non-integrable cosets. This observation suggests that the gravity/CYBE
correspondence can be extended beyond integrable cases.Comment: 21 pages, no figure, LaTeX, v2:clarifications and references added,
v3:minor corrections, further clarifications adde
Integrable sigma models and perturbed coset models
Sigma models arise frequently in particle physics and condensed-matter
physics as low-energy effective theories. In this paper I compute the exact
free energy at any temperature in two hierarchies of integrable sigma models in
two dimensions. These theories, the SU(N)/SO(N) and O(2P)/O(P) x O(P) models,
are asymptotically free and exhibit charge fractionalization. When the
instanton coupling theta=pi, they flow to the SU(N)_1 and O(2P)_1 conformal
field theories, respectively. I also generalize the free energy computation to
massive and massless perturbations of the coset conformal field theories
SU(N)_k/SO(N)_{2k} and O(2P)_k/O(P)_k x O(P)_k.Comment: 39 pages, 6 figure
Harmonic equiangular tight frames comprised of regular simplices
An equiangular tight frame (ETF) is a sequence of unit-norm vectors in a
Euclidean space whose coherence achieves equality in the Welch bound, and thus
yields an optimal packing in a projective space. A regular simplex is a simple
type of ETF in which the number of vectors is one more than the dimension of
the underlying space. More sophisticated examples include harmonic ETFs which
equate to difference sets in finite abelian groups. Recently, it was shown that
some harmonic ETFs are comprised of regular simplices. In this paper, we
continue the investigation into these special harmonic ETFs. We begin by
characterizing when the subspaces that are spanned by the ETF's regular
simplices form an equi-isoclinic tight fusion frame (EITFF), which is a type of
optimal packing in a Grassmannian space. We shall see that every difference set
that produces an EITFF in this way also yields a complex circulant conference
matrix. Next, we consider a subclass of these difference sets that can be
factored in terms of a smaller difference set and a relative difference set. It
turns out that these relative difference sets lend themselves to a second,
related and yet distinct, construction of complex circulant conference
matrices. Finally, we provide explicit infinite families of ETFs to which this
theory applies
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