49 research outputs found
Renormalization schemes for SFT solutions
In this paper, we examine the space of renormalization schemes compatible
with the Kiermaier and Okawa [arXiv:0707.4472] framework for constructing Open
String Field Theory solutions based on marginal operators with singular
self-OPEs. We show that, due to freedom in defining the renormalization scheme
which tames these singular OPEs, the solutions obtained from the KO framework
are not necessarily unique. We identify a multidimensional space of SFT
solutions corresponding to a single given marginal operator.Comment: 41 pages, 1 figur
Entanglement entropy on a fuzzy sphere with a UV cutoff
We introduce a UV cutoff into free scalar field theory on the noncommutative
(fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows
us to control the effective nonlocality scale of the theory. In the resulting
fuzzy geometry, we establish which degrees of freedom lie within a specific
geometric subregion and compute the associated vacuum entanglement entropy.
Entanglement entropy for regions smaller than the effective nonlocality scale
is extensive, while entanglement entropy for regions larger than the effective
nonlocality scale follows the area law. This reproduces features previously
obtained in the strong coupling regime through holography. We also show that
mutual information is unaffected by the UV cutoff.Comment: Significantly revised with improved methodology, 16 pages, 8 figure
Entanglement entropy on the fuzzy sphere
We obtain entanglement entropy on the noncommutative (fuzzy) two-sphere. To
define a subregion with a well defined boundary in this geometry, we use the
symbol map between elements of the noncommutative algebra and functions on the
sphere. We find that entanglement entropy is not proportional to the length of
the region's boundary. Rather, in agreement with holographic predictions, it is
extensive for regions whose area is a small (but fixed) fraction of the total
area of the sphere. This is true even in the limit of small noncommutativity.
We also find that entanglement entropy grows linearly with N, where N is the
size of the irreducible representation of SU(2) used to define the fuzzy
sphere.Comment: 18 pages, 7 figures. v3 to appear in JHEP. Clarified statements about
UV/IR mixing and interpretation in terms of degrees of freedom on the fuzzy
sphere vs. matrix degrees of freedom, fixed some typos and added reference
Noncommutative spaces and matrix embeddings on flat R^{2n+1}
We conjecture an embedding operator which assigns, to any 2n+1 hermitian
matrices, a 2n-dimensional hypersurface in flat (2n + 1)-dimensional Euclidean
space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding
to N D0-branes. Points on the emergent hypersurface correspond to zero
eigenstates of the embedding operator, which have an interpretation as coherent
states underlying the emergent noncommutative geometry. Using this
correspondence, all physical properties of the emergent D(2n)-brane can be
computed. We apply our conjecture to noncommutative flat and spherical spaces.
As a by-product, we obtain a construction of a rotationally symmetric flat
noncommutative space in 4 dimensions.Comment: 14 pages, no figures. v2: added references and a clarificatio