Free quantum fields in 4D and Calabi-Yau spaces - INSPIRE

DataBETA

Free quantum fields in 4D and Calabi-Yau spaces

May 11, 2017

6 pages

Published in:

Phys.Rev.Lett. 119 (2017) 16, 161602

Published: Oct 16, 2017

e-Print:

1705.04039 [hep-th]

DOI:

10.1103/PhysRevLett.119.161602

View in:

ADS Abstract Service

reference search11 citations

Citations per year

Abstract: (APS)

We develop general counting formulas for primary fields in free four dimensional (4D) scalar conformal field theory (CFT). Using a duality map between primary operators in scalar field theory and multivariable polynomial functions subject to differential constraints, we identify a sector of holomorphic primary fields corresponding to polynomial functions on a class of permutation orbifolds. These orbifolds have palindromic Hilbert series, which indicates they are Calabi-Yau orbifolds. We construct the unique top-dimensional holomorphic form expected from the Calabi-Yau property. This sector includes and extends previous constructions of infinite families of primary fields. We sketch the generalization of these results to free 4D vector and matrix CFTs.

Note:

6 pages

field theory: conformal
field theory: scalar
operator: primary
space: Calabi-Yau
dimension: 4
holomorphic
orbifold
duality

References(23)

Figures(0)

[1]

CFT $_4$ as $SO(4,2)$ -invariant TFT $_2$

- Nucl.Phys.B 890 (2014) 302-349
•
e-Print:
- 1403.6646
•
DOI:
- 10.1016/j.nuclphysb.2014.11.013

[2]

Interactions as intertwiners in 4D QFT

- JHEP 03 (2016) 165
•
e-Print:
- 1512.00652
•
DOI:
- 10.1007/JHEP03(2016)165

[3]

I. Frenkel
,
M. Libine

- Adv.Math. 218 (2008) 1806
•
DOI:
- 10.1016/j.aim.2008.03.021

[4]

Higher spin gauge theories in four-dimensions, three-dimensions, and two-dimensions

Mikhail A. Vasiliev
(
- Lebedev Inst.
)

- Int.J.Mod.Phys.D 5 (1996) 763-797
•
e-Print:
- hep-th/9611024
•
DOI:
- 10.1142/S0218271896000473

[5]

AdS dual of the critical O(N) vector model

I.R. Klebanov
(
- Princeton U.
)
,
A.M. Polyakov
(
- Princeton U.
)

- Phys.Lett.B 550 (2002) 213-219
•
e-Print:
- hep-th/0210114
•
DOI:
- 10.1016/S0370-2693(02)02980-5

[6]

Holography in 4D (super) higher spin theories and a test via cubic scalar couplings

E. Sezgin
(
- Texas A-M
)
,
P. Sundell
(
- Uppsala U.
)

- JHEP 07 (2005) 044
•
e-Print:
- hep-th/0305040
•
DOI:
- 10.1088/1126-6708/2005/07/044

[7]

The $\epsilon$ -expansion from conformal field theory

Slava Rychkov
(
- CERN and
- Ecole Normale Superieure and
- UPMC, Paris (main)
)
,
Zhong Ming Tan
(
- Ecole Normale Supérieure, Paris
)

- J.Phys.A 48 (2015) 29, 29FT01
•
e-Print:
- 1505.00963
•
DOI:
- 10.1088/1751-8113/48/29/29FT01

[8]

$\epsilon$ -expansions near three dimensions from conformal field theory

- JHEP 11 (2015) 040
•
e-Print:
- 1506.06616
•
DOI:
- 10.1007/JHEP11(2015)040

[9]

$\epsilon$ -Expansion in the Gross-Neveu model from conformal field theory

Sudip Ghosh
(
- Tata Inst.
)
,
Rajesh Kumar Gupta
(
- ICTP, Trieste
)
,
Kasi Jaswin
(
- Tata Inst.
)
,
Amin A. Nizami
(
- Tata Inst.
)

- JHEP 03 (2016) 174
•
e-Print:
- 1510.04887
•
DOI:
- 10.1007/JHEP03(2016)174

[10]

$\epsilon$ -Expansion in the Gross-Neveu CFT

Avinash Raju
(
- Bangalore, Indian Inst. Sci.
)

- JHEP 10 (2016) 097
•
e-Print:
- 1510.05287
•
DOI:
- 10.1007/JHEP10(2016)097

[11]

Classical equation of motion and Anomalous dimensions at leading order

Keita Nii
(
- Harish-Chandra Res. Inst.
)

- JHEP 07 (2016) 107
•
e-Print:
- 1605.08868
•
DOI:
- 10.1007/JHEP07(2016)107

[12]

Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM

G.P. Korchemsky
(
- Saclay, SPhT
)

- Lett.Math.Phys. 99 (2012) 425-453
•
e-Print:
- 1012.4000
•
DOI:
- 10.1007/s11005-011-0516-7

[13]

EPFL Lectures on Conformal Field Theory in Dimensions, New York,

S. Rychkov

[14]

Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory

V.K. Dobrev
(
- Princeton U.
)
,
V.B. Petkova
(
- Sofiya, Inst. Nucl. Res.
)
,
S.G. Petrova
(
- Sofiya, Inst. Nucl. Res.
)
,
I.T. Todorov
(
- Princeton, Inst. Advanced Study
)

- Phys.Rev.D 13 (1976) 887
•
DOI:
- 10.1103/PhysRevD.13.887

[15]

Spinning Conformal Correlators

Miguel S. Costa
(
- Porto U., Astron. Dept. and
- Porto U.
)
,
Joao Penedones
(
- Perimeter Inst. Theor. Phys.
)
,
David Poland
(
- Harvard U., Phys. Dept.
)
,
Slava Rychkov
(
)

- JHEP 11 (2011) 071
•
e-Print:
- 1107.3554
•
DOI:
- 10.1007/JHEP11(2011)071

[16]

Representations and Invariants of the Classical Groups

R. Goodman
,
N.R. Wallach

[17]

Quite a Character: The Spectrum of Yang-Mills on S3

Taylor H. Newton
(
- Brown U.
)
,
Marcus Spradlin
(
- Brown U.
)

- Phys.Lett.B 672 (2009) 382-385
•
e-Print:
- 0812.4693
•
DOI:
- 10.1016/j.physletb.2009.01.044

[18]

Counting and construction of holomorphic primary fields in free CFT4 from rings of functions on Calabi-Yau orbifolds

- JHEP 08 (2017) 077
•
e-Print:
- 1705.06702
•
DOI:
- 10.1007/JHEP08(2017)077

[19]

Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT

Konstantinos Roumpedakis
(
- YITP, Stony Brook
)

- JHEP 07 (2017) 109
•
e-Print:
- 1612.08115
•
DOI:
- 10.1007/JHEP07(2017)109

[20]

Diagonal free field matrix correlators, global symmetries and giant gravitons

- JHEP 04 (2009) 089
•
e-Print:
- 0806.1911
•
DOI:
- 10.1088/1126-6708/2009/04/089

[21]

SQCD: A Geometric Apercu

James Gray
(
- Oxford U., Theor. Phys.
)
,
Amihay Hanany
(
- Imperial Coll., London
)
,
Yang-Hui He
(
- Oxford U., Theor. Phys. and
- Oxford U. and
- Oxford U., Inst. Math.
)
,
Vishnu Jejjala
(
- IHES, Bures-sur-Yvette
)
,
Noppadol Mekareeya
(
- Imperial Coll., London
)

- JHEP 05 (2008) 099
•
e-Print:
- 0803.4257
•
DOI:
- 10.1088/1126-6708/2008/05/099

[22]

The Hilbert Series of Adjoint SQCD

- Nucl.Phys.B 825 (2010) 52-97
•
e-Print:
- 0812.2315
•
DOI:
- 10.1016/j.nuclphysb.2009.09.016

[23]

R. Stanley

- Adv.Math. 28 (1978) 57
•
DOI:
- 10.1016/0001-8708(78)90045-2