Bootstrap bound for conformal multi-flavor QCD on lattice

Nakayama, Yu

doi:10.1007/jhep07(2016)038

Cited by 29 publications

(36 citation statements)

References 27 publications

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“…According to theorem 2.1, this means that the primary of W * should transform in the same representation as O 2 , i.e. 44 On the other hand, the 43 The complication in the case of odd d is that when O is a fermion, we cannot choose the external operators so that there is a single tensor structure on each side of the seed block. Instead, the minimum is two.…”

Section: Expression For Seed Blocksmentioning

confidence: 99%

“…This is related to the fact that the irreducible fermionic representations of SO(d − 1) are necessarily chiral when d is odd. 44 Such a W * always exists. In fact, there are infinitely many choices differing by the value of j, and the W * with minimal j is obtained by prepending a 0 to the list of Dynkin labels of ρ2 (in the natural ordering where the vector label is the first and the spinor labels are the last).…”

Section: Expression For Seed Blocksmentioning

confidence: 99%

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Weight shifting operators and conformal blocks

Karateev

Kravchuk

Simmons-Duffin

2018

J. High Energ. Phys.

167

369

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We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an application, we derive a formula for a general conformal block (with arbitrary internal and external representations) in terms of derivatives of blocks for external scalars. In particular, our formula gives new expressions for "seed conformal blocks" in 3d and 4d CFTs. We also find simple derivations of identities between external-scalar blocks with different dimensions and internal spins. We comment on additional applications, including deriving recursion relations for general conformal blocks, reducing inversion formulae for spinning operators to inversion formulae for scalars, and deriving identities between general 6j symbols (Racah-Wigner coefficients/"crossing kernels") of the conformal group.

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Section: Expression For Seed Blocksmentioning

confidence: 99%

Section: Expression For Seed Blocksmentioning

confidence: 99%

Weight shifting operators and conformal blocks

Karateev

Kravchuk

Simmons-Duffin

2018

J. High Energ. Phys.

167

369

View full text Add to dashboard Cite

show abstract

“…refs. [4,10,[17][18][19][20][21][22]33], where bounds of this kind (and others) have been determined with the derivative method using both linear and semi-definite programming.…”

Section: D Cftsmentioning

confidence: 99%

The effective bootstrap

Echeverri

Harling

Serone

2016

J. High Energ. Phys.

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Abstract:We study the numerical bounds obtained using a conformal-bootstrap method -advocated in ref.[1] but never implemented so far -where different points in the plane of conformal cross ratios z andz are sampled. In contrast to the most used method based on derivatives evaluated at the symmetric point z =z = 1/2, we can consistently "integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations. We test this "effective" bootstrap by studying the 3D Ising and O(n) vector models and bounds on generic 4D CFTs, for which extensive results are already available in the literature. We also determine the scaling dimensions of certain scalar operators in the O(n) vector models, with n = 2, 3, 4, which have not yet been computed using bootstrap techniques.

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“…These derive from imposing crossing symmetry constraints on the four-point function of a scalar (meson) operator Φ ij transforming according to the bifundamental representation of the SUðN f Þ × SUðN f Þ global symmetry group. From the work of Nakayama [22] the bounds are γ Ã m < 1.79 for N f ¼ 8 and γ Ã m < 1.88 for N f ¼ 100. Clearly the values of the safe anomalous dimensions lie comfortably below this bound.…”

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confidence: 99%

Conformal window 2.0: The large Nf safe story

Antipin

Sannino

2018

Phys. Rev. D

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We extend the phase diagram of SU(N) gauge-fermion theories as a function of the number of flavors and colors to the region in which asymptotic freedom is lost. We argue, using large N f results, for the existence of an ultraviolet interacting fixed point at a sufficiently large number of flavors opening up to a second ultraviolet conformal window in the number of flavors vs colors phase diagram. We first review the state-ofthe-art for the large N f beta function and then estimate the lower boundary of the ultraviolet window. The theories belonging to this new region are examples of safe non-Abelian quantum electrodynamics, termed here safe QCD. Therefore, according to Wilson, they are fundamental. An important critical quantity is the fermion mass anomalous dimension at the ultraviolet fixed point that we determine at leading order in 1=N f . We discover that its value is comfortably below the bootstrap bound. We also investigate the Abelian case and find that at the potential ultraviolet fixed point the related fermion mass anomalous dimension has a singular behavior suggesting that a more careful investigation of its ultimate fate is needed. DOI: 10.1103/PhysRevD.97.116007 The discovery of asymptotic freedom [1,2] has been a landmark in our understanding of fundamental interactions. By fundamental we mean that, following Wilson [3,4], these theories are valid at arbitrary short and long distance scales. Asymptotic freedom has therefore guided a great deal of Standard Model (SM) extensions. Likewise the discovery of four-dimensional asymptotically safe field theories [5] constitutes an important alternative to asymptotic freedom. It has opened the door to new ways to generalize the Standard Model [6][7][8][9][10][11] with impact in dark matter physics and cosmology [10]. The essential feature of an asymptotically safe completion of the SM is that it tames its high energy behavior dynamically uplifting to the status of a truly fundamental field theory. In practice this means that theory does not have a physical cutoff and that the UV theory is mapped into an interacting conformal field theory. What kind of theories can be asymptotically safe and what are their fundamental features? We know already that scalar field theories (Higgs-like) are unsafe, and that quantum electrodynamics is unsafe as well, at least in perturbation theory.In the original construction [5] elementary scalars and their induced Yukawa interactions played a crucial role in helping make the overall gauge-Yukawa theory safe. Here we will investigate, instead, the ultraviolet fate of gaugefermion theories at a finite number of colors but a very large number of flavors of both Abelian and non-Abelian nature.We start by considering an SUðN c Þ gauge theory with N f fermions transforming according to a given representation of the gauge group. We will assume that asymptotic freedom is lost, meaning that the number of flavors is larger than N AF f > 11C G =ð4T R Þ, where the first coefficient of the beta function changes sign. We do not need to ...

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Bootstrap bound for conformal multi-flavor QCD on lattice

Cited by 29 publications

References 27 publications

Weight shifting operators and conformal blocks

Weight shifting operators and conformal blocks

The effective bootstrap

Conformal window 2.0: The large Nf safe story

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