scholarly journals Emergent conformal symmetry in nonunitary random dynamics of free fermions

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Xiao Chen ◽  
Yaodong Li ◽  
Matthew P. A. Fisher ◽  
Andrew Lucas
Keyword(s):  
Conformal Symmetry ◽  
Free Fermions ◽  
Random Dynamics

scholarly journals Resolving modular flow: a toolkit for free fermions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Johanna Erdmenger ◽  
Pascal Fries ◽  
Ignacio A. Reyes ◽  
Christian P. Simon
Keyword(s):  
Complex Analysis ◽  
Conformal Symmetry ◽  
Standard Technique ◽  
Analytic Structure ◽  
Point Function ◽  
Free Fermions ◽  
Modular Evolution ◽  
Non Local ◽  
Kms Condition ◽  
New Formula

Abstract Modular flow is a symmetry of the algebra of observables associated to space-time regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in 1 + 1 dimensions, working directly from the resolvent, a standard technique in complex analysis. We present novel results — not fixed by conformal symmetry — for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.

scholarly journals Extended Conformal Symmetry of the One-Dimensional Bose Gas

1997 ◽  
Vol 12 (29) ◽  
pp. 2153-2159 ◽  
Author(s):  
Milena Maule ◽  
Stefano Sciuto
Keyword(s):  
Cartan Subalgebra ◽  
Conformal Symmetry ◽  
Hard Core ◽  
Bose Gas ◽  
Effective Hamiltonian ◽  
Coupling Constant ◽  
Free Fermions ◽  
One Dimensional ◽  
First Order ◽  
The One

We show that the low-lying excitations of the one-dimensional Bose gas are described, at all orders in a 1/N expansion and at the first order in the inverse of the coupling constant, by an effective Hamiltonian written in terms of an extended conformal algebra, namely the Cartan subalgebra of the [Formula: see text] algebra. This enables us to construct the first interaction term which corrects the Hamiltonian of the free fermions equivalent to a hard-core boson system.

scholarly journals Simplicity of AdS supergravity at one loop

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Luis F. Alday ◽  
Xinan Zhou
Keyword(s):  
Closed Form ◽  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Loop Level ◽  
Level Data ◽  
Space Limit ◽  
Loop Amplitude

Abstract We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the $$ \left\langle {\mathcal{O}}_2^{SG}{\mathcal{O}}_2^{SG}{\mathcal{O}}_p^{SG}{\mathcal{O}}_p^{SG}\right\rangle $$ O 2 SG O 2 SG O p SG O p SG correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

scholarly journals Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Alessandro Torrielli
Keyword(s):  
Spectral Problem ◽  
Transfer Matrix ◽  
Arbitrary Number ◽  
Free Fermion ◽  
Nearest Neighbour ◽  
Bogoliubov Transformation ◽  
Free Fermions ◽  
New Models ◽  
Lower Dimensional

Abstract In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS3, mixed-flux relativistic AdS3 and massless AdS2. We also attack the class of models akin to AdS5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

scholarly journals Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Charles B. Thorn
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Spin Chain ◽  
Discrete Dynamical System ◽  
Heisenberg Spin ◽  
Free Fermions ◽  
Heisenberg Spin Chain ◽  
Delta Sigma ◽  
Special Cases ◽  
Quantized String

Abstract Although the energy spectrum of the Heisenberg spin chain on a circle defined by$$ H=\frac{1}{4}\sum \limits_{k=1}^M\left({\sigma}_k^x{\sigma}_{k+1}^x+{\sigma}_k^y{\sigma}_{k+1}^y+\Delta {\sigma}_k^z{\sigma}_{k+1}^z\right) $$ H = 1 4 ∑ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether M ∈ 4ℕ + r, where r = −1, 0, 1, 2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M1< M and M − M1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case ∆ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R0. We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for ∆ ≠ 0 is a change in the compactification radius R0→ R∆. As ∆ → −1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.

scholarly journals Notes on gravity multiplet correlators in AdS3 × S3

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Congkao Wen ◽  
Shun-Qing Zhang
Keyword(s):  
Recursion Relation ◽  
Conformal Symmetry ◽  
Flat Space ◽  
The Other ◽  
Tree Level ◽  
Space Limit ◽  
Compact Expression ◽  
Tensor Multiplet ◽  
R Symmetry

Abstract We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.

scholarly journals Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion

2000 ◽  
Vol 479 (4) ◽  
pp. 411-420 ◽  
Author(s):  
J.A. Helayel-Neto ◽  
A. Penna-Firme ◽  
I.L. Shapiro
Keyword(s):  
Effective Action ◽  
Conformal Symmetry ◽  
Scalar Gravity

scholarly journals Conformal symmetry for rotating D-branes

2009 ◽  
Vol 679 (4) ◽  
pp. 390-395 ◽  
Author(s):  
Li-Ming Cao ◽  
Yoshinori Matsuo ◽  
Takuya Tsukioka ◽  
Chul-Moon Yoo
Keyword(s):  
Conformal Symmetry
Sign in / Sign up

Export Citation Format

Share Document