Spontaneous symmetry breaking in tensor theories

We continue the study of the bosonic O(N) 3 model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant φ 4 composite operators, known as tetrahedron, pillow and double-trace. As shown in [1, 2], the tetrahedron operator is exactly marginal in the large-N limit and for a purely imaginary tetrahedron coupling a line of real infrared fixed points (parametrized by the absolute value of the tetrahedron coupling) is found for the other two couplings. These fixed points have real critical exponents and a real spectrum of bilinear operators, satisfying unitarity constraints. This raises the question whether at large-N the model is unitary, despite the tetrahedron coupling being imaginary. In this paper, we first rederive the above results by a different regularization and renormalization scheme. We then discuss the operator mixing for composite operators and we give a perturbative proof of conformal invariance of the model at the infrared fixed points by adapting a similar proof from the long-range Ising model. At last, we identify the scaling operators at the fixed point and compute the two-and three-point functions of φ 4 and φ 2 composite operators. The correlations have the expected conformal behavior and the OPE coefficients are all real, reinforcing the claim that the large-N CFT is unitary.

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“…(3.8) 4 Spontaneous symmetry breaking in tensor field theories has been so far not much explored, but see refs. [17,68,69].…”

Section: Jhep06(2020)113mentioning

confidence: 99%

Conformal symmetry and composite operators in the O(N )3 tensor field theory

Benedetti

Gurău

Suzuki

2020

J. High Energ. Phys.

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“…(3.7) 4 Spontaneous symmetry breaking in tensor field theories has been so far not much explored, but see Ref. [17,68,69].…”

Section: The Two-point Functionmentioning

confidence: 99%

Conformal Symmetry and Composite Operators in the $O(N)^3$ Tensor Field Theory

Benedetti,

Gurau,

Suzuki

2020

Preprint

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We continue the study of the bosonic O(N ) 3 model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant φ 4 composite operators, known as tetrahedron, pillow and double-trace. As shown in [1,2], the tetrahedron operator is exactly marginal in the large-N limit and for a purely imaginary tetrahedron coupling a line of real infrared fixed points (parametrized by the absolute value of the tetrahedron coupling) is found for the other two couplings. These fixed points have real critical exponents and a real spectrum of bilinear operators, satisfying unitarity constraints. This raises the question whether at large-N the model is unitary, despite the tetrahedron coupling being imaginary.In this paper, we first rederive the above results by a different regularization and renormalization scheme. We then discuss the operator mixing for composite operators and we give a perturbative proof of conformal invariance of the model at the infrared fixed points by adapting a similar proof from the long-range Ising model. At last, we identify the scaling operators at the fixed point and compute the two-and three-point functions of φ 4 and φ 2 composite operators. The correlations have the expected conformal behavior and the OPE coefficients are all real, reinforcing the claim that the large-N CFT is unitary.

show abstract

“…[19] for a review), but the ones arising in tensor models are relatively new, and for the moment tightly associated to the large-N limit. On the other hand, SSB in tensor models has been mostly unexplored, with the only exception being the work of Diaz and Rosabal [20], which however, as we will argue in the following, did not provide interesting symmetry breaking solutions from the point of view of the large-N limit.…”

Section: Introductionmentioning

confidence: 98%

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
13
0
11
0
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We study classical and quantum (at large-N ) field equations of bosonic tensor models with quartic interactions and O(N ) 3 symmetry. Among various possible patterns of spontaneous symmetry breaking we highlight an SO(3) invariant solution, with the tensor field expressed in terms of the Wigner 3jm symbol. We argue that such solution has a special role in the large-N limit, as in particular its scaling in N can provide an on-shell justification for the melonic large-N limit of the two-particle irreducible effective action in a broken phase.

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Spontaneous symmetry breaking in tensor theories

Cited by 11 publications

References 105 publications

Conformal symmetry and composite operators in the O(N )3 tensor field theory

Conformal symmetry and composite operators in the O(N )3 tensor field theory

Conformal Symmetry and Composite Operators in the $O(N)^3$ Tensor Field Theory

SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
13
0
11
0
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Spontaneous symmetry breaking in tensor theories

Cited by 11 publications

References 105 publications

Conformal symmetry and composite operators in the O(N )3 tensor field theory

Conformal symmetry and composite operators in the O(N )3 tensor field theory

Conformal Symmetry and Composite Operators in the $O(N)^3$ Tensor Field Theory

SO(3) -invariant phase of the O(N)3Benedetti1, Costa2 2020Phys. Rev. D130110View full textAdd to dashboardCite

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SO(3) -invariant phase of the O(N)3
Benedetti
¹
,
Costa
²

2020
Phys. Rev. D
13
0
11
0
View full text Add to dashboard Cite