O(N) models with boundary interactions and their long range generalizations

Self Cite

Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O(N) model in general dimension d, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

Section: Jhep11(2020)118supporting

confidence: 86%

CFT in AdS and boundary RG flows

Giombi

Khanchandani

2020

Self Cite

“…25) which is in perfect agreement with the correction (3.20) that we computed for a φ 2 and the crossing relations (2.13). Using(3.24) to compute the two-point function of1 2 (∂ y φ)2 …”

supporting

confidence: 90%

“…Without loss of generality, we can assume there is at most one boundary operator of dimension ∆ 1 with b φÔ = 0, that we denote as O 1 , and similarly for ∆ 2 , the corresponding operator being denoted as O 2 . 4 As observed in [25], the scaling dimensions of these operators add up to d − 1, which suggests that the two operators might be thought of as a 'shadow pair'. In the next subsection we will show that also their three-point functions are compatible with such a 'shadow relation'.…”

Section: Jhep12(2020)182mentioning

confidence: 84%

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Bootstrapping boundary-localized interactions

Behan

Pietro

Lauria

et al. 2020

We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

“…See refs. [28,29] for recent investigations although such a theory provides an important cross check already in [8]. Another important class of boundary CFTs that are free in the bulk are graphene like: they have a 4d photon and 3d charged matter (see e.g.…”

Section: Jhep09(2020)126mentioning

confidence: 99%

The O(N ) model with ϕ6 potential in ℝ2 × ℝ+

Herzog

Kobayashi

2020

We study the large N limit of O(N ) scalar field theory with classically marginal ϕ6 interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large N . We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal ϕ6 coupling.