### Abstract

The KPZ formula [V.G. Knizhnik, A.M. Polyakov, and A.B. Zamolodchikov, Mod. Phys. Lett. A 3 (1988) 819] shows that coupling central charge c=1 spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on c. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of F^{3} planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins. Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the "wrong" c value. We might then expect to see the critical exponents appropriate to the c value used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the lsing, tricritical lsing and 3-state Potts modles. © 1999 Published by Elsevier Science B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 271-275 |

Number of pages | 5 |

Journal | Physics Letters B |

Volume | 460 |

Issue number | 3-4 |

Publication status | Published - 1999 |

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*Physics Letters B*,

*460*(3-4), 271-275.

}

*Physics Letters B*, vol. 460, no. 3-4, pp. 271-275.

**The wrong kind of gravity.** / Janke, Wolfhard; Johnston, Desmond A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The wrong kind of gravity

AU - Janke, Wolfhard

AU - Johnston, Desmond A.

PY - 1999

Y1 - 1999

N2 - The KPZ formula [V.G. Knizhnik, A.M. Polyakov, and A.B. Zamolodchikov, Mod. Phys. Lett. A 3 (1988) 819] shows that coupling central charge c=1 spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on c. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of F3 planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins. Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the "wrong" c value. We might then expect to see the critical exponents appropriate to the c value used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the lsing, tricritical lsing and 3-state Potts modles. © 1999 Published by Elsevier Science B.V. All rights reserved.

AB - The KPZ formula [V.G. Knizhnik, A.M. Polyakov, and A.B. Zamolodchikov, Mod. Phys. Lett. A 3 (1988) 819] shows that coupling central charge c=1 spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on c. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of F3 planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins. Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the "wrong" c value. We might then expect to see the critical exponents appropriate to the c value used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the lsing, tricritical lsing and 3-state Potts modles. © 1999 Published by Elsevier Science B.V. All rights reserved.

UR - http://www.scopus.com/inward/record.url?scp=0001268406&partnerID=8YFLogxK

M3 - Article

VL - 460

SP - 271

EP - 275

JO - Physics Letters B

JF - Physics Letters B

SN - 0370-2693

IS - 3-4

ER -