Anomaly polynomial of general 6D SCFTs

Ohmori, Kantaro; Shimizu, Hiroyuki; Tachikawa, Yuji; Yonekura, Kazuya

doi:10.1093/ptep/ptu140

Cited by 187 publications

(403 citation statements)

References 57 publications

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“…For that we require the anomaly polynomial of the rank Q E-string theory. This was computed in [32,33], who found it to be, We use the notation C 2 (R), C 2 (L ) for the second Chern classes in the fundamental representation of the SU(2) R and SU(2) L symmetries, respectively. Here SU(2) R denotes the R-symmetry and SU (2) L denotes the global symmetry of the higher rank E-string theory.…”

Section: E-stringmentioning

confidence: 99%

E‐String Theory on Riemann Surfaces

Kim

Razamat

Vafa

et al. 2017

Fortschritte der Physik

103

380

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We study compactifications of the 6d E-string theory, the theory of a small E 8 instanton, to four dimensions. In particular we identify N = 1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E 8 flavor symmetry. This sheds light on emergent symmetries in a number of 4d N = 1 SCFTs (including the 'E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries.

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Section: E-stringmentioning

confidence: 99%

E‐String Theory on Riemann Surfaces

Kim

Razamat

Vafa

et al. 2017

Fortschritte der Physik

103

380

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“…Consequently we lose no information by restricting our attention to the four-point function of the scalar superconformal primary, which is a dramatically simpler object. 16 This is a huge simplification in bootstrap studies and has already been exploited for maximally superconformal field theories in four [62] and three [83,84] dimensions. The results described in this section rely heavily on the previous works [48,49].…”

Section: The Four-point Function Of Stress Tensor Multipletsmentioning

confidence: 99%

“…The superconformal Ward identities impose no further constraints on these functions. 16 In fact, the technology to bootstrap four-point functions involving external tensorial operators, while conceptually straightforward, has not yet been fully developed. Rapid progress is being made in the area-see [103][104][105][106][107][108][109][110][111][112][113][114][115][116][117].…”

Section: A Structure Of the Four-point Functionmentioning

confidence: 99%

The (2, 0) superconformal bootstrap

et al. 2016

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We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 25) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A 1 theory is the unique unitary solution to the crossing symmetry equation at c ¼ 25. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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“…The anomaly polynomials of E-string theories have been computed in [42] (see also [43] for more general N = (1, 0) theories). Expanding in powers of N , the anomaly polynomial takes the form 8 36) where A 8 (1) is the anomaly polynomial of a free N = (2, 0) tensor multiplet (3.8), e(N M ) is the Euler class of the normal bundle, and…”

Section: E-string Theoriesmentioning

confidence: 99%

Supersymmetric Casimir energy and the anomaly polynomial

Bobev

Bullimore

Kim

2015

J. High Energ. Phys.

108

207

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We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D−1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

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Anomaly polynomial of general 6D SCFTs

Cited by 187 publications

References 57 publications

E‐String Theory on Riemann Surfaces

E‐String Theory on Riemann Surfaces

The (2, 0) superconformal bootstrap

Supersymmetric Casimir energy and the anomaly polynomial

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