Holography and the Coleman-Mermin-Wagner theorem

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.066008· OSTI ID:21421216

Anninos, Dionysios; Hartnoll, Sean A ^[1]; Iqbal, Nabil ^[2]

---

1. Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts 02138 (United States)
2. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

In 2+1 dimensions at finite temperature, spontaneous symmetry breaking of global symmetries is precluded by large thermal fluctuations of the order parameter. The holographic correspondence implies that analogous effects must also occur in 3+1 dimensional theories with gauged symmetries in certain curved spacetimes with horizon. By performing a one loop computation in the background of a holographic superconductor, we show that bulk quantum fluctuations wash out the classical order parameter at sufficiently large distance scales. The low temperature phase is seen to exhibit algebraic long-range order. Beyond the specific example we study, holography suggests that IR singular quantum fluctuations of the fields and geometry will play an interesting role for many 3+1 dimensional asymptotically anti-de Sitter spacetimes with planar horizon.

• OSTI ID: 21421216
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevD.82.066008; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
FLUCTUATIONS
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
HOLOGRAPHY
ORDER PARAMETERS
SPACE-TIME
SUPERCONDUCTORS
SYMMETRY
SYMMETRY BREAKING
THREE-DIMENSIONAL CALCULATIONS
DIMENSIONLESS NUMBERS
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
SPACE
VARIATIONS