Fluctuations and Energy Shifts in the Bethe Ansatz
arXiv:hep-th/0506243 · doi:10.1016/j.physletb.2005.07.015
Abstract
We study fluctuations and finite size corrections for the ferromagnetic thermodynamic limit in the Bethe ansatz for the Heisenberg XXX1/2 spin chain, which is the AdS/CFT dual of semiclassical spinning strings. For this system we derive the standard quantum mechanical formula which expresses the energy shift as a sum over fluctuation energies. As an example we apply our results to the simplest, one-cut solution of this system and derive its spectrum of fluctuations.
8 pages, 1 figure, v2: comparison to string theory improved, reference added
References in corpus (10)
- Bethe Ansatz for Quantum Strings
- The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
- Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
- On one-loop correction to energy of spinning strings in S^5
- Complete Spectrum of Long Operators in N=4 SYM at One Loop
- Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector
- Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
- Higher-Loop Integrability in N=4 Gauge Theory
- Spin Chain for Quantum Strings
- Rational three-spin string duals and non-anomalous finite size effects
Cited by in corpus (29)
- Foundations of the AdS_5 x S^5 Superstring. Part I
- Quantum corrections to the string Bethe ansatz
- On Quantum Corrections to Spinning Strings and Bethe Equations
- Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
- Green-Schwarz Strings in TsT-transformed backgrounds
- Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
- Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
- Complete 1-loop test of AdS/CFT
- Tailoring Three-Point Functions and Integrability III. Classical Tunneling
- Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
- How Accurate is the Quantum String Bethe Ansatz?
- The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
- Y-system and Quasi-Classical Strings
- Constructing the AdS/CFT dressing factor
- Strings as Multi-Particle States of Quantum Sigma-Models
- Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
- 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
- Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
- Double Scaling and Finite Size Corrections in sl(2) Spin Chain
- Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
- Macroscopic (and Microscopic) Massless Modes
- Quantum Stability for the Heisenberg Ferromagnet
- On the Scattering Phase for AdS_5 x S^5 Strings
- Aspects of Integrability in AdS/CFT Duality
- Finite-size corrections to the rotating string and the winding state
- On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
- Anomalous dimensions of finite size field strength operators in N=4 SYM
- Generalized Gribov-Lipatov Reciprocity and AdS/CFT
- Remarks on the geometrical properties of semiclassically quantized strings