Built on

A. M. Polyakov, “Quantum Geometry of Bosonic Strings,” Phys. Lett. 103B
1981
Earlier work this paper cites.
H. Osborn, “Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories,” Nucl. Phys. B 363
1991
Earlier work this paper cites.
F. Larsen and F. Wilczek, “Geometric entropy, wave functionals, and fermions,” Annals Phys. 243
1995
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
J. M. Maldacena, Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
K. Gawedzki, “Lectures on Conformal Field Theoreis”, Quantum Fields and Strings: A Course for Mathematicians Vol.2, American Mathematical Society, 1999. https://pdfs.semanticscholar.org/cca2/78b7cf71c3e9730852d3bf5f64233aa1db9e.pdf
1999
Earlier work this paper cites.
I. R. Klebanov and E. Witten, “AdS / CFT correspondence and symmetry breaking,” Nucl. Phys. B 556
1999
Earlier work this paper cites.
J. de Boer, E. P. Verlinde and H. L. Verlinde, “On the holographic renormalization group,” JHEP 0008
2000
Earlier work this paper cites.
K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19
2002
Earlier work this paper cites.
S. R. Das and A. Jevicki, “Large N collective fields and holography,” Phys. Rev. D 68
2003
Earlier work this paper cites.
G. Vidal,“A class of quantum many-body states that can be efficiently simulated,” Phys. Rev. Lett. 101
2007
Earlier work this paper cites.
D. Friedan and A. Konechny, “Gradient formula for the beta-function of 2d quantum field theory,” J. Phys. A 43
Original
2010
Earlier work this paper cites.
I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” JHEP 1106
Original
2011
Earlier work this paper cites.

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Later among the works it cites.
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M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, “Distance between Quantum States and Gauge-Gravity Duality,” Phys. Rev. Lett. 115
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Later among the works it cites.
P. Rath, “Holographic Complexity,” Perimeter Scholars International essay (unpublished) (June 2016)
2016
Later among the works it cites.
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2018

Path-Integral Complexity for Perturbed CFTs

Bhattacharyya, Arpan, Caputa, Pawel, Das, Sumit R. et al.

Understand

In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators.

We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories.
Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings.
Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence.

Built on

A. M. Polyakov, “Quantum Geometry of Bosonic Strings,” Phys. Lett. 103B
1981
Earlier work this paper cites.
H. Osborn, “Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories,” Nucl. Phys. B 363
1991
Earlier work this paper cites.
F. Larsen and F. Wilczek, “Geometric entropy, wave functionals, and fermions,” Annals Phys. 243
1995
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
J. M. Maldacena, Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
K. Gawedzki, “Lectures on Conformal Field Theoreis”, Quantum Fields and Strings: A Course for Mathematicians Vol.2, American Mathematical Society, 1999. https://pdfs.semanticscholar.org/cca2/78b7cf71c3e9730852d3bf5f64233aa1db9e.pdf
1999
Earlier work this paper cites.
I. R. Klebanov and E. Witten, “AdS / CFT correspondence and symmetry breaking,” Nucl. Phys. B 556
1999
Earlier work this paper cites.
J. de Boer, E. P. Verlinde and H. L. Verlinde, “On the holographic renormalization group,” JHEP 0008
2000
Earlier work this paper cites.
K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19
2002
Earlier work this paper cites.
S. R. Das and A. Jevicki, “Large N collective fields and holography,” Phys. Rev. D 68
2003
Earlier work this paper cites.
G. Vidal,“A class of quantum many-body states that can be efficiently simulated,” Phys. Rev. Lett. 101
2007
Earlier work this paper cites.
D. Friedan and A. Konechny, “Gradient formula for the beta-function of 2d quantum field theory,” J. Phys. A 43
Original
2010
Earlier work this paper cites.
I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” JHEP 1106
Original
2011
Earlier work this paper cites.