Boundary Liouville Field Theory I. Boundary State and Boundary Two-point Function

By V. Fateev, A. Zamolodchikov, A. Zamolodchikov. 2000

429 citations recorded by the source corpus.

Liouville conformal field theory is considered with conformal boundary. There is a family of conformal boundary conditions parameterized by the boundary cosmological constant, so that observables depend on the dimensional ratios of boundary and bulk cosmological constants. The disk geometry is considered. We present an explicit expression for the expectation value of a bulk operator inside the disk and for the two-point function of boundary operators. We comment also on the properties of the degenrate boundary operators. Possible applications and further developments are discussed. In particular, we present exact expectation values of the boundary operators in the boundary sin-Gordon model.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/69066e168ef18d47e16fc01c898409f95b2b80b5

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In Applied Mathematics

1. D. Gaiotto
2. T. Nishioka
3. J. Teschner
4. J. Maldacena
5. H. Verlinde
6. John McGreevy
7. N. Seiberg
8. I. Klebanov

In Astronomy and Astrophysics

1. T. Takayanagi
2. J. Maldacena
3. D. Stanford
4. Y. Nakayama
5. T. Nishioka
6. D. Harlow
7. R. Myers
8. S. Shenker

In Nuclear and High Energy Physics

1. J. Maldacena
2. T. Takayanagi
3. E. Witten
4. D. Stanford
5. Y. Nakayama
6. T. Nishioka
7. D. Gaiotto
8. D. Harlow

Citations in the corpus

• Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “The boundary action in the Liouville theory [64] reads”
• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models (2009, background): “ring requirement that the total central charge of Liouville theory plus minimal matter equals c = 26 eventually fixes b = q p q. There are two distinct types of boundary conditions in Liouville theory [63, 64]. There is a one–parameter family of Neumann boundary conditions, the so–called FZZT branes,”
• Liouville Field Theory — A decade after the revolution (2004, methodology): “These ideas were applied to the boundary Liouville theory in [2], [155].”
• AdS bubbles, entropy and closed string tachyons (2006, methodology): “tachyon) in type II or other string theories, we can apply the same boost argument in the presence of the null dilaton and the boundary Liouville term µB R @� dz e − bX 1 [74].”
• Classical and quantum D-branes in 2D string theory (2003, background): “The corresponding boundary states were constructed in [14].”
• Rolling tachyons from Liouville theory (2003, neutral): “In addition, we rewrite the infinite sum by means of some simple trigonometric identities, lnΥb(α) ∼ lnYβ(α)− πi 2 ( Qb 2 − α )2 − i ∞ ∑ n=1 1 n sin 2πniα β + 1 n cot πn β2 cos 2πniα β up to some constant depending only on b.”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “The rules for including D-brane boundaries do not have a clear origin in gravity; we must rely upon the matrix integral description of JT gravity to understand how to properly (31)These branes are also closely related to branes in topological string theories described by matrix models [64, 65, 66, 6”
• The Annular Report on Non-Critical String Theory (2003, methodology): “Thus, matrix model results are fully compatible with the Liouville bootstrap of [ 22 , 23, 24].”
• D-brane Decay in Two-Dimensional String Theory (2003, methodology): “D-branes [ 34-36 ]. The D-branes studied in [34,35] (and [25]) are extended in the Liouville”