Critical scaling in the large- N O ( N ) model in higher dimensions and its possible connection to quantum gravity

214

Abstract:We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0|N ) supergroup theories are holographically dual to an exotic variant of type IIB string theory on dS 3,2 ×S 5 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for N = 2 SU(N |M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

Section: Jhep02(2018)050mentioning

confidence: 99%

Section: Jhep02(2018)050mentioning

confidence: 99%

Section: Jhep02(2018)050mentioning

confidence: 99%

Section: Jhep02(2018)050mentioning

confidence: 99%

Section: Consequences For Negative Branesmentioning

confidence: 99%

See 3 more Smart Citations

Negative branes, supergroups and the signature of spacetime

Dijkgraaf

Heidenreich

Jefferson

et al. 2018

214

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey

Chang

Fluder

Lin

et al. 2018

123

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counterterms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F -theorem and possibly a C-theorem in five-dimensional superconformal theories.

The free σCFTs

Guerrieri¹,

Petkou²,

Wen³

2016

We introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in d dimensions. We argue that these theories can be consistently defined as free CFTs for even d ≥ 4. We use OPE techniques to study their spectrum and show that for d → ∞ it matches that of free bosonic CFTs in d = 6 and d = 4 dimensions. For these σCFTs we calculate c T in d = 6, 8, 10 and 12 dimensions using the OPE and also a direct construction of their higher-derivative energy momentum tensors. Our results agree with the general proposal of arXiv:1601.07198.Free conformal field theories (CFTs) can be intriguing. This is one of the main lessons higher-spin holography 1 has taught us. For all their apparent simplicity, free CFTs emerge holographically as the result of a complicated symmetry that makes possible the consistent interaction of infinite towers of higher-spin gauge fields. And even though symmetry breaking may be the most physically relevant property of a theory, the exploitation of its symmetric phase usually yields interesting knowledge.In this work we initiate the study of two peculiar free CFTs that are universally connected to free massless scalars φ(x) and Dirac fermions ψ(x) in d dimensions. For those free theories, the simplest composite fields one can construct are 2 φ 2 (x) andψ(x)ψ(x) and parametrize the usual mass deformations.Considering then x-dependent mass terms such as d d xσ 2 (x)φ 2 (x) and d d xσ 1 (x)ψ(x)ψ(x) one elevates σ 2 (x) and σ 1 (x) to genuine scalar fields that determine the effective action of the massive phase. Moreover, since the canonical scaling dimensions of φ(x) and ψ(x) are ∆ φ = d 2 − 1 and ∆ ψ = d−1 2 , the fields σ 2 (x) and σ 1 (x) exhibit universal scaling behaviour in any d, namely ∆ σ 2 = 2 and ∆ σ 1 = 1. In the CFT language σ 2 (x) and σ 1 (x) are the shadows 3 of the composites φ 2 (x) andψ(x)ψ(x) respectively.The fields σ 2 (x) and σ 1 (x) are not part of the spectrum of the corresponding free CFTs for any d.They show up, however, in the spectrum of non-trivial bosonic and fermionic CFTs in 2 < d < 6 [4][5][6][7] where they generically acquire anomalous dimensions. Remarkably, taking the strict N → ∞ limit of the non-trivial theories one is left with theories where all fields have canonical dimensions and yet σ 2 (x) and σ 1 (x) are still in the spectrum replacing φ 2 (x) andψ(x)ψ(x) respectively. Nevertheless, at least for the above range of dimensions, it has been noticed that all the non-trivial CFT models do become free field theories for d = 2, 4, 6 and hence it is natural to ask about the fate of the σ-fields in these cases. For the bosonic O(N ) vector model in 2 < d < 4 this has been partially discussed in [8]. It was there shown that if one starts with both of the fields φ 2 (x) and σ 2 (x) in the theory, the second one decouples in the free field theory limit and the first one becomes redundant at the non-trivial fixed point. This mechanism was connected to the O(N ) → O(N − 1) global symmetr...