# 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)

- 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. doi:10.1007/jhep11(2017)121.
```

```
Berenstein, David, and Miller, Alexandra. Mon .
"Superposition induced topology changes in quantum gravity". United States. doi: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 = {2017},

month = {11}

}

*Citation information provided by*

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#### Figures / Tables:

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_{1}, $n$

_{2}, $\tilde{n}$

_{2}. . . are quantized and can be taken to be integers.

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

##
LLM magnons

journal, March 2016

- de Mello Koch, Robert; Mathwin, Christopher; van Zyl, Hendrik J. R.
- Journal of High Energy Physics, Vol. 2016, Issue 3

##
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

##
A new double-scaling limit of super-Yang–Mills theory and pp-wave strings

journal, November 2002

- Kristjansen, C.; Plefka, J.; Semenoff, G. W.
- Nuclear Physics B, Vol. 643, Issue 1-3

##
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

##
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

##
Reconstructing spacetime from the hologram, even in the classical limit, requires physics beyond the Planck scale

journal, October 2016

- Berenstein, David; Miller, Alexandra
- International Journal of Modern Physics D, Vol. 25, Issue 12

##
Matrix string theory

journal, September 1997

- Dijkgraaf, Robbert; Verlinde, Erik; Verlinde, Herman
- Nuclear Physics B, Vol. 500, Issue 1-3

##
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

##
Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

journal, June 2017

- Berenstein, David; Miller, Alexandra
- Physical Review Letters, Vol. 118, Issue 26

##
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

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*