Kähler uniformization from holographic renormalization group flows of M5-branes

Fluder, Martin

doi:10.1007/jhep08(2018)046

Title: Kähler uniformization from holographic renormalization group flows of M5-branes

Abstract

In this study, we initiate the study of holographic renormalization group flows for the metric of four-manifolds. In particular, we derive a set of equations which govern the evolution of a generic Kähler four-manifold along the renormalization group flow in seven-dimensional gauged supergravity. The physical eleven-dimensional M-theory setup is given by a stack of M5-branes wrapping a calibrated Kähler four-cycle inside a Calabi-Yau threefold. By topologically twisting the theory in the ultraviolet, we may choose an arbitrary Kähler metric on the four-cycle as an asymptotic boundary condition. We find that at the infrared fixed point, we reach a Kähler-Einstein metric, which can be interpreted as an indication of “uniformizing” behavior of the flow.

Authors:

Fluder, Martin ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. of Theoretical Physics

Publication Date:: Fri Aug 10 00:00:00 EDT 2018

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1501465

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT Correspondence; M-Theory; Renormalization Group; Supergravity Models

Citation Formats


                    Fluder, Martin. Kähler uniformization from holographic renormalization group flows of M5-branes.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep08(2018)046.

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                    Fluder, Martin. Kähler uniformization from holographic renormalization group flows of M5-branes.  United States.  https://doi.org/10.1007/jhep08(2018)046

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                    Fluder, Martin. Fri .  
"Kähler uniformization from holographic renormalization group flows of M5-branes".  United States.  https://doi.org/10.1007/jhep08(2018)046.  https://www.osti.gov/servlets/purl/1501465.

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@article{osti_1501465,

  title        = {Kähler uniformization from holographic renormalization group flows of M5-branes},

  author       = {Fluder, Martin},

  abstractNote = {In this study, we initiate the study of holographic renormalization group flows for the metric of four-manifolds. In particular, we derive a set of equations which govern the evolution of a generic Kähler four-manifold along the renormalization group flow in seven-dimensional gauged supergravity. The physical eleven-dimensional M-theory setup is given by a stack of M5-branes wrapping a calibrated Kähler four-cycle inside a Calabi-Yau threefold. By topologically twisting the theory in the ultraviolet, we may choose an arbitrary Kähler metric on the four-cycle as an asymptotic boundary condition. We find that at the infrared fixed point, we reach a Kähler-Einstein metric, which can be interpreted as an indication of “uniformizing” behavior of the flow.},

  doi          = {10.1007/jhep08(2018)046},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 8,

  volume       = 2018,

  place        = {United States},

  year         = {Fri Aug 10 00:00:00 EDT 2018},

  month        = {Fri Aug 10 00:00:00 EDT 2018}

}

Copy to clipboard

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Works referenced in this record:

Comments on string dynamics in six dimensions
journal, July 1996

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 471, Issue 1-2
DOI: 10.1016/0550-3213(96)00189-7

N = 2 dualities
journal, August 2012

Gaiotto, Davide
Journal of High Energy Physics, Vol. 2012, Issue 8
DOI: 10.1007/JHEP08(2012)034

Moduli of half conformally flat structures
journal, December 1993

Itoh, Mitsuhiro
Mathematische Annalen, Vol. 296, Issue 1
DOI: 10.1007/BF01445130

The topology of four-dimensional manifolds
journal, January 1982

Freedman, Michael Hartley
Journal of Differential Geometry, Vol. 17, Issue 3
DOI: 10.4310/jdg/1214437136

A supergravity dual of a (1,0) field theory in six dimensions
journal, October 1998

Berkooz, Micha
Physics Letters B, Vol. 437, Issue 3-4
DOI: 10.1016/S0370-2693(98)00913-7

Kähler-Einstein metrics with positive scalar curvature
journal, September 1997

Tian, Gang
Inventiones Mathematicae, Vol. 130, Issue 1
DOI: 10.1007/s002220050176

Gauged maximally extended supergravity in seven dimensions
journal, August 1984

Pernici, M.; Pilch, K.; van Nieuwenhuizen, P.
Physics Letters B, Vol. 143, Issue 1-3
DOI: 10.1016/0370-2693(84)90813-X

Fivebranes wrapped on associative three-cycles
journal, April 2001

Acharya, Bobby S.; Gauntlett, Jerome P.; Kim, Nakwoo
Physical Review D, Vol. 63, Issue 10
DOI: 10.1103/PhysRevD.63.106003

Topological quantum field theory
journal, September 1988

Witten, Edward
Communications in Mathematical Physics, Vol. 117, Issue 3
DOI: 10.1007/BF01223371

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 431, Issue 3
DOI: 10.1016/0550-3213(94)90214-3

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
journal, May 1978

Yau, Shing-Tung
Communications on Pure and Applied Mathematics, Vol. 31, Issue 3
DOI: 10.1002/cpa.3160310304

Three-manifolds with positive Ricci curvature
journal, January 1982

Hamilton, Richard S.
Journal of Differential Geometry, Vol. 17, Issue 2
DOI: 10.4310/jdg/1214436922

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Communications in Mathematical Physics, Vol. 299, Issue 1
DOI: 10.1007/s00220-010-1071-2

Calibrations and Intersecting Branes
journal, May 1999

Gibbons, G. W.; Papadopoulos, G.
Communications in Mathematical Physics, Vol. 202, Issue 3
DOI: 10.1007/s002200050597

BPS M5-branes as defects for the 3d-3d correspondence
journal, November 2014

Bah, Ibrahima; Gabella, Maxime; Halmagyi, Nick
Journal of High Energy Physics, Vol. 2014, Issue 11
DOI: 10.1007/JHEP11(2014)112

M theory and singularities of exceptional holonomy manifolds
journal, March 2004

Acharya, Bobby S.; Gukov, Sergei
Physics Reports, Vol. 392, Issue 3
DOI: 10.1016/j.physrep.2003.10.017

D-branes and topological field theories
journal, March 1996

Bershadsky, M.; Vafa, C.; Sadov, V.
Nuclear Physics B, Vol. 463, Issue 2-3
DOI: 10.1016/0550-3213(96)00026-0

An obstruction to the existence of Einstein K�hler metrics
journal, October 1983

Futaki, A.
Inventiones Mathematicae, Vol. 73, Issue 3
DOI: 10.1007/BF01388438

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Maldacena, Juan
International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
DOI: 10.1023/A:1026654312961

Nonlinear models in 2 + ε dimensions
journal, September 1985

Friedan, Daniel Harry
Annals of Physics, Vol. 163, Issue 2
DOI: 10.1016/0003-4916(85)90384-7

Branes and Calibrated Geometries
journal, May 1999

Gauntlett, Jerome P.; Lambert, Neil D.; West, Peter C.
Communications in Mathematical Physics, Vol. 202, Issue 3
DOI: 10.1007/s002200050596

Supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds
journal, November 1996

Becker, Katrin; Becker, Melanie; Morrison, David R.
Nuclear Physics B, Vol. 480, Issue 1-2
DOI: 10.1016/S0550-3213(96)00491-9

AdS/CFT dual pairs from M5-branes on Riemann surfaces
journal, June 2012

Bah, Ibrahima; Beem, Christopher; Bobev, Nikolay
Physical Review D, Vol. 85, Issue 12
DOI: 10.1103/PhysRevD.85.121901

Holographic Uniformization
journal, February 2013

Anderson, Michael T.; Beem, Christopher; Bobev, Nikolay
Communications in Mathematical Physics, Vol. 318, Issue 2
DOI: 10.1007/s00220-013-1675-4

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
Communications in Mathematical Physics, Vol. 325, Issue 2
DOI: 10.1007/s00220-013-1863-2

Consistent nonlinear KK reduction of 11d supergravity on AdS7×S4 and self-duality in odd dimensions
journal, December 1999

Nastase, Horatiu; Vaman, Diana; Nieuwenhuizen, Peter van
Physics Letters B, Vol. 469, Issue 1-4
DOI: 10.1016/S0370-2693(99)01266-6

Monopoles and four-manifolds
journal, January 1994

Witten, Edward
Mathematical Research Letters, Vol. 1, Issue 6
DOI: 10.4310/MRL.1994.v1.n6.a13

Fivebranes, membranes and non-perturbative string theory
journal, December 1995

Becker, Katrin; Becker, Melanie; Strorninger, Andrew
Nuclear Physics B, Vol. 456, Issue 1-2
DOI: 10.1016/0550-3213(95)00487-1

The Yang-Mills Equations over Riemann Surfaces
journal, March 1983

Atiyah, M. F.; Bott, R.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 308, Issue 1505
DOI: 10.1098/rsta.1983.0017

M-fivebranes wrapped on supersymmetric cycles. II
journal, March 2002

Gauntlett, Jerome P.; Kim, Nakwoo
Physical Review D, Vol. 65, Issue 8
DOI: 10.1103/PhysRevD.65.086003

Exact Two-Dimensional Superconformal $R$ Symmetry and $c$ Extremization
journal, February 2013

Benini, Francesco; Bobev, Nikolay
Physical Review Letters, Vol. 110, Issue 6
DOI: 10.1103/PhysRevLett.110.061601

AdS spacetimes from wrapped M5 branes
journal, November 2006

Gauntlett, Jerome P.; Conamhna, Oisín A. P. Mac; Mateos, Toni
Journal of High Energy Physics, Vol. 2006, Issue 11
DOI: 10.1088/1126-6708/2006/11/053

Embedding AdS black holes in ten and eleven dimensions
journal, October 1999

Cveticˇ, M.; Duff, M. J.; Hoxha, P.
Nuclear Physics B, Vol. 558, Issue 1-2
DOI: 10.1016/S0550-3213(99)00419-8

Supergravity Description of Field Theories on Curved Manifolds and a no go Theorem
journal, February 2001

Maldacena, Juan; NuÑEz, Carlos
International Journal of Modern Physics A, Vol. 16, Issue 05
DOI: 10.1142/S0217751X01003937

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 426, Issue 1
DOI: 10.1016/0550-3213(94)90124-4

Global geometry of the supersymmetric ${AdS}_{3} / {CFT}_{2}$ correspondence in M-theory
journal, August 2007

Figueras, Pau; Mac Conamhna, Oisín A. P.; Ó Colgáin, Eoin
Physical Review D, Vol. 76, Issue 4
DOI: 10.1103/PhysRevD.76.046007

Deformation of K�hler matrics to K�hler-Einstein metrics on compact K�hler manifolds
journal, June 1985

Cao, Huai-Dong
Inventiones Mathematicae, Vol. 81, Issue 2
DOI: 10.1007/BF01389058

Liouville Correlation Functions from Four-Dimensional Gauge Theories
journal, January 2010

Alday, Luis F.; Gaiotto, Davide; Tachikawa, Yuji
Letters in Mathematical Physics, Vol. 91, Issue 2
DOI: 10.1007/s11005-010-0369-5

Three dimensional manifolds, Kleinian groups and hyperbolic geometry
journal, May 1982

Thurston, William P.
Bulletin of the American Mathematical Society, Vol. 6, Issue 3
DOI: 10.1090/S0273-0979-1982-15003-0

Four-dimensional SCFTs from M5-branes
journal, June 2012

Bah, Ibrahima; Beem, Christopher; Bobev, Nikolay
Journal of High Energy Physics, Vol. 2012, Issue 6
DOI: 10.1007/JHEP06(2012)005

3D supergravity from wrapped M5-branes
journal, March 2016

Karndumri, Parinya; Ó Colgáin, Eoin
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/JHEP03(2016)188

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points
journal, April 2014

Beem, Christopher; Gadde, Abhijit
Journal of High Energy Physics, Vol. 2014, Issue 4
DOI: 10.1007/JHEP04(2014)036

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
Communications in Mathematical Physics, Vol. 325, Issue 2
DOI: 10.1007/s00220-013-1863-2

3-Manifolds and 3d indices
journal, January 2013

Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 5
DOI: 10.4310/atmp.2013.v17.n5.a3

Embedding AdS Black Holes in Ten and Eleven Dimensions
text, January 1999

Cvetic, M.; Duff, M. J.; Hoxha, P.
arXiv
DOI: 10.48550/arxiv.hep-th/9903214

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Title: Kähler uniformization from holographic renormalization group flows of M5-branes

Abstract

Citation Formats

Comments on string dynamics in six dimensions journal, July 1996

N = 2 dualities journal, August 2012

Moduli of half conformally flat structures journal, December 1993

The topology of four-dimensional manifolds journal, January 1982

A supergravity dual of a (1,0) field theory in six dimensions journal, October 1998

Kähler-Einstein metrics with positive scalar curvature journal, September 1997

Gauged maximally extended supergravity in seven dimensions journal, August 1984

Fivebranes wrapped on associative three-cycles journal, April 2001

Topological quantum field theory journal, September 1988

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD journal, December 1994

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I journal, May 1978

Three-manifolds with positive Ricci curvature journal, January 1982

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory journal, July 2010

Calibrations and Intersecting Branes journal, May 1999

BPS M5-branes as defects for the 3d-3d correspondence journal, November 2014

M theory and singularities of exceptional holonomy manifolds journal, March 2004

D-branes and topological field theories journal, March 1996

An obstruction to the existence of Einstein K�hler metrics journal, October 1983

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Nonlinear models in 2 + ε dimensions journal, September 1985

Branes and Calibrated Geometries journal, May 1999

Supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds journal, November 1996

AdS/CFT dual pairs from M5-branes on Riemann surfaces journal, June 2012

Holographic Uniformization journal, February 2013

Gauge Theories Labelled by Three-Manifolds journal, December 2013

Consistent nonlinear KK reduction of 11d supergravity on AdS7×S4 and self-duality in odd dimensions journal, December 1999

Monopoles and four-manifolds journal, January 1994

Fivebranes, membranes and non-perturbative string theory journal, December 1995

The Yang-Mills Equations over Riemann Surfaces journal, March 1983

M-fivebranes wrapped on supersymmetric cycles. II journal, March 2002

Exact Two-Dimensional Superconformal R Symmetry and c Extremization journal, February 2013

AdS spacetimes from wrapped M5 branes journal, November 2006

Embedding AdS black holes in ten and eleven dimensions journal, October 1999

Supergravity Description of Field Theories on Curved Manifolds and a no go Theorem journal, February 2001

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory journal, September 1994

Global geometry of the supersymmetric AdS 3 / CFT 2 correspondence in M-theory journal, August 2007

Deformation of K�hler matrics to K�hler-Einstein metrics on compact K�hler manifolds journal, June 1985

Liouville Correlation Functions from Four-Dimensional Gauge Theories journal, January 2010

Three dimensional manifolds, Kleinian groups and hyperbolic geometry journal, May 1982

Four-dimensional SCFTs from M5-branes journal, June 2012

3D supergravity from wrapped M5-branes journal, March 2016

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points journal, April 2014

Gauge Theories Labelled by Three-Manifolds journal, December 2013

3-Manifolds and 3d indices journal, January 2013

Embedding AdS Black Holes in Ten and Eleven Dimensions text, January 1999

Comments on string dynamics in six dimensions
journal, July 1996

N = 2 dualities
journal, August 2012

Moduli of half conformally flat structures
journal, December 1993

The topology of four-dimensional manifolds
journal, January 1982

A supergravity dual of a (1,0) field theory in six dimensions
journal, October 1998

Kähler-Einstein metrics with positive scalar curvature
journal, September 1997

Gauged maximally extended supergravity in seven dimensions
journal, August 1984

Fivebranes wrapped on associative three-cycles
journal, April 2001

Topological quantum field theory
journal, September 1988

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
journal, May 1978

Three-manifolds with positive Ricci curvature
journal, January 1982

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

Calibrations and Intersecting Branes
journal, May 1999

BPS M5-branes as defects for the 3d-3d correspondence
journal, November 2014

M theory and singularities of exceptional holonomy manifolds
journal, March 2004

D-branes and topological field theories
journal, March 1996

An obstruction to the existence of Einstein K�hler metrics
journal, October 1983

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Nonlinear models in 2 + ε dimensions
journal, September 1985

Branes and Calibrated Geometries
journal, May 1999

Supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds
journal, November 1996

AdS/CFT dual pairs from M5-branes on Riemann surfaces
journal, June 2012

Holographic Uniformization
journal, February 2013

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

Consistent nonlinear KK reduction of 11d supergravity on AdS7×S4 and self-duality in odd dimensions
journal, December 1999

Monopoles and four-manifolds
journal, January 1994

Fivebranes, membranes and non-perturbative string theory
journal, December 1995

The Yang-Mills Equations over Riemann Surfaces
journal, March 1983

M-fivebranes wrapped on supersymmetric cycles. II
journal, March 2002

Exact Two-Dimensional Superconformal $R$ Symmetry and $c$ Extremization
journal, February 2013

AdS spacetimes from wrapped M5 branes
journal, November 2006

Embedding AdS black holes in ten and eleven dimensions
journal, October 1999

Supergravity Description of Field Theories on Curved Manifolds and a no go Theorem
journal, February 2001

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994

Global geometry of the supersymmetric ${AdS}_{3} / {CFT}_{2}$ correspondence in M-theory
journal, August 2007

Deformation of K�hler matrics to K�hler-Einstein metrics on compact K�hler manifolds
journal, June 1985

Liouville Correlation Functions from Four-Dimensional Gauge Theories
journal, January 2010

Three dimensional manifolds, Kleinian groups and hyperbolic geometry
journal, May 1982

Four-dimensional SCFTs from M5-branes
journal, June 2012

3D supergravity from wrapped M5-branes
journal, March 2016

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points
journal, April 2014

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

3-Manifolds and 3d indices
journal, January 2013

Embedding AdS Black Holes in Ten and Eleven Dimensions
text, January 1999