Hamiltonian truncation in Anti-de Sitter spacetime

We study the boundary critical behavior of conformal field theories of interacting fermions in the Gross-Neveu universality class. By a Weyl transformation, the problem can be studied by placing the CFT in an anti de Sitter space background. After reviewing some aspects of free fermion theories in AdS, we use both large N methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the Gross-Neveu CFT. At large N and general dimension d, we find three distinct boundary conformal phases. Near four dimensions, where the CFT is described by the Wilson-Fisher fixed point of the Gross-Neveu-Yukawa model, two of these phases correspond respectively to the choice of Neumann or Dirichlet boundary condition on the scalar field, while the third one corresponds to the case where the bulk scalar field acquires a classical expectation value. One may flow between these boundary critical points by suitable relevant boundary deformations. We compute the AdS free energy on each of them, and verify that its value is consistent with the boundary version of the F-theorem. We also compute some of the BCFT observables in these theories, including bulk two-point functions of scalar and fermions, and four-point functions of boundary fermions.

“…Throughout this paper, we are always going to assume that the bulk theory is at its critical point 2. See also[16][17][18][19][20] for related studies of QFT and CFT in AdS.…”

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confidence: 99%

Fermions in AdS and Gross-Neveu BCFT

Giombi

Helfenberger

Khanchandani

2022

“…A natural extension of our work is to consider Z 2 -breaking deformations of minimal model boundary conditions in AdS. The simplest example would be the magnetic deformation of the Ising model, which was studied in AdS with Hamiltonian truncation in [36]. More generally, we could combine the thermal and magnetic deformations hence studying Ising field theory [66].…”

Section: Discussionmentioning

confidence: 99%

“…Note that in going from the upper half-plane to AdS2 the stress-energy tensor is unchanged (see e.g [36]…”

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confidence: 99%

See 1 more Smart Citation

A bootstrap study of minimal model deformations

Antunes,

Lauria,

van Rees

2024

For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional CFTs, focusing on deformations of the tricritical and ordinary Ising model. We provide non-perturbative constraints for the boundary correlation functions of these flows and compare them with conformal perturbation theory in the vicinity of the fixed points. We also reproduce a completely general constraint on the sign of the $$T\overline{T }$$ deformation in two dimensions.

“…See for example refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], as well as the reviews [26,27]. A particularly important focus for research in this area has been on the development of effective Hamiltonians for improving the accuracy of Hamiltonian Truncation estimates [4,[28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Effective Hamiltonians and Counterterms for Hamiltonian Truncation

Miró

Ingoldby

2023

We outline a procedure for applying Hamiltonian Truncation to Quantum Field Theories (QFTs) that have UV divergences. To do this, we derive a novel representation of an Effective Hamiltonian which makes manifest some of its important properties (e.g. the non-perturbative matching of the spectra between the UV theory and the theory described by the Effective Hamiltonian). We check the consistency of our procedure using Conformal Perturbation Theory. Finally we comment on how the Effective Hamiltonian, which incorporates non-local interactions, describes a local QFT.