Superposition induced topology changes in quantum gravity
Abstract
We show that superpositions of classical states in quantum gravity with fixed topology can lead to new classical states with a different topology. We study this phenomenon in a particular limit of the LLM geometries. In this limit, the UV complete minisuperspace of allowed quantum states is exactly given by the Hilbert space of a free chiral boson in two dimensions. We construct this chiral boson purely in terms of combinatorial objects associated with the permutation group. As a byproduct of this analysis, we rederive the Murnaghan-Nakayama rule for characters of the permutation group. We are able to express this rule in terms of operator relations for raising and lowering operators on the Hilbert space of states in a free fermion basis. Our construction provides a preferred notion of bulk locality by studying an appropriate notion of D-brane state generating functions. We describe how multi-droplet LLM geometries with different topologies give new classical limits of the free chiral boson, even though they can be written as superpositions of coherent states with trivial topology. As a consequence, topology cannot be accessed by a single operator measurement in this quantum system. In conclusion, we study other non-linear measurements in the quantum wave-function,more »
- Authors:
-
- Univ. of California, Santa Barbara, CA (United States). Physics Dept.
- Publication Date:
- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1499190
- Grant/Contract Number:
- SC0011702
- 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: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Matrix Models; Models of Quantum Gravity
Citation Formats
Berenstein, David, and Miller, Alexandra. Superposition induced topology changes in quantum gravity. United States: N. p., 2017.
Web. doi:10.1007/jhep11(2017)121.
Berenstein, David, & Miller, Alexandra. Superposition induced topology changes in quantum gravity. United States. https://doi.org/10.1007/jhep11(2017)121
Berenstein, David, and Miller, Alexandra. Mon .
"Superposition induced topology changes in quantum gravity". United States. https://doi.org/10.1007/jhep11(2017)121. https://www.osti.gov/servlets/purl/1499190.
@article{osti_1499190,
title = {Superposition induced topology changes in quantum gravity},
author = {Berenstein, David and Miller, Alexandra},
abstractNote = {We show that superpositions of classical states in quantum gravity with fixed topology can lead to new classical states with a different topology. We study this phenomenon in a particular limit of the LLM geometries. In this limit, the UV complete minisuperspace of allowed quantum states is exactly given by the Hilbert space of a free chiral boson in two dimensions. We construct this chiral boson purely in terms of combinatorial objects associated with the permutation group. As a byproduct of this analysis, we rederive the Murnaghan-Nakayama rule for characters of the permutation group. We are able to express this rule in terms of operator relations for raising and lowering operators on the Hilbert space of states in a free fermion basis. Our construction provides a preferred notion of bulk locality by studying an appropriate notion of D-brane state generating functions. We describe how multi-droplet LLM geometries with different topologies give new classical limits of the free chiral boson, even though they can be written as superpositions of coherent states with trivial topology. As a consequence, topology cannot be accessed by a single operator measurement in this quantum system. In conclusion, we study other non-linear measurements in the quantum wave-function, based on uncertainty and entanglement between modes of the chiral boson, that can be used as order parameters to measure the topology of such states.},
doi = {10.1007/jhep11(2017)121},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {Mon Nov 20 00:00:00 EST 2017},
month = {Mon Nov 20 00:00:00 EST 2017}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Building up spacetime with quantum entanglement
journal, June 2010
- Van Raamsdonk, Mark
- General Relativity and Gravitation, Vol. 42, Issue 10
Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
journal, January 1998
- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 3
Eternal black holes in anti-de Sitter
journal, April 2003
- Maldacena, Juan
- Journal of High Energy Physics, Vol. 2003, Issue 04
Entanglement entropy converges to classical entropy around periodic orbits
journal, March 2016
- Asplund, Curtis T.; Berenstein, David
- Annals of Physics, Vol. 366
Folds, bosonization and non-triviality of the classical limit of 2D string theory
journal, January 1996
- Das, Sumit R.; Mathur, Samir D.
- Physics Letters B, Vol. 365, Issue 1-4
Open spin chains for giant gravitons and relativity
journal, August 2013
- Berenstein, David; Dzienkowski, Eric
- Journal of High Energy Physics, Vol. 2013, Issue 8
Singularities and closed time-like curves in type-IIB 1/2 BPS geometries
journal, September 2005
- Milanesi, Giuseppe; O'Loughlin, Martin
- Journal of High Energy Physics, Vol. 2005, Issue 09
Bits, matrices and 1/ N
journal, December 2003
- Verlinde, Herman
- Journal of High Energy Physics, Vol. 2003, Issue 12
An infalling observer in AdS/CFT
journal, October 2013
- Papadodimas, Kyriakos; Raju, Suvrat
- Journal of High Energy Physics, Vol. 2013, Issue 10
Anti de Sitter space and holography
journal, January 1998
- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
Half-BPS giants, free fermions and microstates of superstars
journal, January 2006
- Suryanarayana, Nemani V.
- Journal of High Energy Physics, Vol. 2006, Issue 01
Quantum foam and topological strings
journal, April 2008
- Iqbal, Amer; Vafa, Cumrun; Nekrasov, Nikita
- Journal of High Energy Physics, Vol. 2008, Issue 04
Quantizing Open Spin Chains with Variable Length and Giant Gravitons in the Anti–de Sitter-Space/Conformal Field-Theory Correspondence
journal, November 2005
- Berenstein, David; Correa, Diego H.; Vázquez, Samuel E.
- Physical Review Letters, Vol. 95, Issue 19
Integrability vs. information loss: a simple example
journal, November 2006
- Balasubramanian, Vijay; Czech, Bartłomiej; Larjo, Klaus
- Journal of High Energy Physics, Vol. 2006, Issue 11
AdS 3 black holes and a stringy exclusion principle
journal, December 1998
- Maldacena, Juan; Strominger, Andrew
- Journal of High Energy Physics, Vol. 1998, Issue 12
Minisuperspace quantization of ``Bubbling AdS" and free fermion droplets
journal, August 2005
- Grant, Lars; Maoz, Liat; Marsano, Joseph
- Journal of High Energy Physics, Vol. 2005, Issue 08
Two-dimensional QCD is a string theory
journal, July 1993
- Gross, David J.; Taylor, Washington
- Nuclear Physics B, Vol. 400, Issue 1-3
Anatomy of bubbling solutions
journal, September 2007
- Skenderis, Kostas; Taylor, Marika
- Journal of High Energy Physics, Vol. 2007, Issue 09
SUSY and Goliath
journal, August 2000
- Grisaru, Marcus T.; Myers, Robert C.; Tafjord, Øyvind
- Journal of High Energy Physics, Vol. 2000, Issue 08
Exact correlators of giant gravitons from dual $N = 4$ SYM theory
journal, January 2001
- Corley, Steve; Jevicki, Antal; Ramgoolam, Sanjaye
- Advances in Theoretical and Mathematical Physics, Vol. 5, Issue 4
On classification of the bubbling geometries
journal, April 2006
- Mosaffa, Amir E.; Sheikh-Jabbari, Mohammad M.
- Journal of High Energy Physics, Vol. 2006, Issue 04
Strings on orbifolds
journal, January 1985
- Dixon, L.; Harvey, J. A.; Vafa, C.
- Nuclear Physics B, Vol. 261
The quantum collective field method and its application to the planar limit
journal, April 1980
- Jevicki, A.; Sakita, B.
- Nuclear Physics B, Vol. 165, Issue 3
Invasion of the giant gravitons from anti-de Sitter space
journal, May 2000
- McGreevy, John; Susskind, Leonard; Toumbas, Nicolaos
- Journal of High Energy Physics, Vol. 2000, Issue 06
Black holes and beyond
journal, November 2012
- Mathur, Samir D.
- Annals of Physics, Vol. 327, Issue 11
Black holes: complementarity or firewalls?
journal, February 2013
- Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph
- Journal of High Energy Physics, Vol. 2013, Issue 2
Cool horizons for entangled black holes
journal, August 2013
- Maldacena, J.; Susskind, L.
- Fortschritte der Physik, Vol. 61, Issue 9
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
Giant Gravitons in Conformal Field Theory
journal, April 2002
- Balasubramanian, Vijay; Berkooz, Micha; Naqvi, Asad
- Journal of High Energy Physics, Vol. 2002, Issue 04
Giant gravitons and the emergence of geometric limits in β-deformations of N = 4 $$ \mathcal{N}=4 $$ SYM
journal, January 2015
- Berenstein, David; Dzienkowski, Eric
- Journal of High Energy Physics, Vol. 2015, Issue 1
A toy model for the AdS/CFT correspondence
journal, July 2004
- Berenstein, David
- Journal of High Energy Physics, Vol. 2004, Issue 07
Bubbling AdS space and 1/2 BPS geometries
journal, October 2004
- Lin, Hai; Lunin, Oleg; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2004, Issue 10
Fermions from half-BPS supergravity
journal, August 2005
- Mandal, Gautam
- Journal of High Energy Physics, Vol. 2005, Issue 08
Large branes in AdS and their field theory dual
journal, August 2000
- Hashimoto, Akikazu; Hirano, Shinji; Itzhaki, N.
- Journal of High Energy Physics, Vol. 2000, Issue 08
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006
- Ryu, Shinsei; Takayanagi, Tadashi
- Physical Review Letters, Vol. 96, Issue 18
Thermodynamics of black holes in anti-de Sitter space
journal, December 1983
- Hawking, S. W.; Page, Don N.
- Communications in Mathematical Physics, Vol. 87, Issue 4
Black holes as effective geometries
journal, October 2008
- Balasubramanian, Vijay; de Boer, Jan; El-Showk, Sheer
- Classical and Quantum Gravity, Vol. 25, Issue 21
Particle creation by black holes
journal, August 1975
- Hawking, S. W.
- Communications In Mathematical Physics, Vol. 43, Issue 3
Elliptic Genera of Symmetric Products and Second Quantized Strings
journal, April 1997
- Dijkgraaf, Robbert; Moore, Gregory; Verlinde, Erik
- Communications in Mathematical Physics, Vol. 185, Issue 1
Schur functions, chiral bosons, and the quantum-Hall-effect edge states
journal, November 1990
- Stone, Michael
- Physical Review B, Vol. 42, Issue 13
Strings on orbifolds (II)
journal, September 1986
- Dixon, L.; Harvey, J.; Vafa, C.
- Nuclear Physics B, Vol. 274, Issue 2
Dirichlet Branes and Ramond-Ramond Charges
journal, December 1995
- Polchinski, Joseph
- Physical Review Letters, Vol. 75, Issue 26
Linearity of holographic entanglement entropy
journal, February 2017
- Almheiri, Ahmed; Dong, Xi; Swingle, Brian
- Journal of High Energy Physics, Vol. 2017, Issue 2
Chronology protection in anti-de Sitter
journal, August 2005
- Caldarelli, Marco M.; Klemm, Dietmar; Silva, Pedro J.
- Classical and Quantum Gravity, Vol. 22, Issue 17
Geometries from Young diagrams
journal, November 2008
- Koch, Robert de Mello
- Journal of High Energy Physics, Vol. 2008, Issue 11
Bouncing Universes in String Theory?
conference, August 2005
- Polchinski, Joseph
- String Theory and Cosmology
Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior
text, January 2015
- Papadodimas, Kyriakos; Raju, Suvrat
- arXiv
Works referencing / citing this record:
Exciting LLM geometries
journal, July 2018
- de Mello Koch, Robert; Huang, Jia-Hui; Tribelhorn, Laila
- Journal of High Energy Physics, Vol. 2018, Issue 7
Emergent classical spacetime from microstates of an incipient black hole
text, January 2018
- Balasubramanian, Vijay; Berenstein, David; Lewkowycz, Aitor
- arXiv
Exciting LLM Geometries
text, January 2018
- Koch, Robert de Mello; Huang, Jia-Hui; Tribelhorn, Laila
- arXiv
Emergent classical spacetime from microstates of an incipient black hole
journal, January 2019
- Balasubramanian, Vijay; Berenstein, David; Lewkowycz, Aitor
- Journal of High Energy Physics, Vol. 2019, Issue 1
Code subspaces for LLM geometries
journal, February 2018
- Berenstein, David; Miller, Alexandra
- Classical and Quantum Gravity, Vol. 35, Issue 6
Quantum information processing and composite quantum fields
journal, January 2019
- Ramgoolam, Sanjaye; Sedlák, Michal
- Journal of High Energy Physics, Vol. 2019, Issue 1
Quantum information processing and composite quantum fields
journal, January 2019
- Ramgoolam, Sanjaye; Sedlák, Michal
- Journal of High Energy Physics, Vol. 2019, Issue 1
Code subspaces for LLM geometries
journal, February 2018
- Berenstein, David; Miller, Alexandra
- Classical and Quantum Gravity, Vol. 35, Issue 6
Semiclassical SL(2) Strings on LLM backgrounds
text, January 2018
- Kim, Minkyoo; van Zyl, Hendrik J. R.
- arXiv