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