Exact lattice bosonization of the double-scaled c=1 matrix model
Abstract
In a recent paper by two of us, it has been shown that entanglement entropy (EE) of matrix quantum mechanics (or, equivalently, of a non-relativistic fermion model) has a natural interpretation in terms of an exact bosonization of the fermion theory in terms of a lattice boson with lattice spacing ∼ 1/N (where N is the rank of the matrix, equal to the number of fermions). The theory of this lattice boson is distinct from a latticized version of the "collective variable'' theory which is formulated in terms of the fermion density ρ(λ) ("collective variable''); it is, in fact, more closely related to the Wigner distribution of the fermions. In this paper, we develop this connection further for the c=1 double scaled matrix model. Even though N becomes infinite, the double scaled theory is described by a boson on a finite and non-uniform lattice spacing, of order ∼ gs(x) ls (where gs(x) ≡ gs cosech2(x/ls) is a position dependent string coupling). We explicitly derive the c=1 EE, as well as the one and two-point functions of fermion density from the lattice boson. The results are explicitly finite, unlike the collective variable theory which is shown to yield divergent answers. Our results suggest that while local observables such as the EE and ⟨ ρ(λ) ⟩, are characterized by a unique short distance scale gs(x) ls, the asymptotic observables such as the S-matrix at every genus are characterized by a short distance scale ls. We show how this arises and discuss a possible interpretation in terms of D0 brane physics.
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BibTeX
@misc{gaikwad2026exact,
title = {{Exact lattice bosonization of the double-scaled $c=1$ matrix model}},
author = {Adwait Gaikwad and Gautam Mandal and Ajay Mohan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34376},
eprint = {2610.34376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact lattice bosonization of the double-scaled c=1 matrix model
AU - Adwait Gaikwad
AU - Gautam Mandal
AU - Ajay Mohan
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34376
UR - https://arxiv.org/abs/2610.34376
AB - In a recent paper by two of us, it has been shown that entanglement entropy (EE) of matrix quantum mechanics (or, equivalently, of a non-relativistic fermion model) has a natural interpretation in terms of an exact bosonization of the fermion theory in terms of a lattice boson with lattice spacing ∼ 1/N (where N is the rank of the matrix, equal to the number of fermions). The theory of this lattice boson is distinct from a latticized version of the "collective variable'' theory which is formulated in terms of the fermion density ρ(λ) ("collective variable''); it is, in fact, more closely related to the Wigner distribution of the fermions. In this paper, we develop this connection further for the c=1 double scaled matrix model. Even though N becomes infinite, the double scaled theory is described by a boson on a finite and non-uniform lattice spacing, of order ∼ g_s(x) l_s (where g_s(x) ≡ g_s cosech^2(x/l_s) is a position dependent string coupling). We explicitly derive the c=1 EE, as well as the one and two-point functions of fermion density from the lattice boson. The results are explicitly finite, unlike the collective variable theory which is shown to yield divergent answers. Our results suggest that while local observables such as the EE and ⟨ ρ(λ) ⟩, are characterized by a unique short distance scale g_s(x) l_s, the asymptotic observables such as the S-matrix at every genus are characterized by a short distance scale l_s. We show how this arises and discuss a possible interpretation in terms of D0 brane physics.
ER -