Non-linear sigma models with anti-de Sitter target spaces
We present evidence that there is a non-trivial fixed point for the AdS D + 1 non-linear sigma model in two dimensions, without any matter fields or additional couplings beyond the standard quadratic action subject to a quadratic constraint. A zero of the beta function, both in the bosonic and super...
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| Published in | Nuclear physics. B Vol. 750; no. 3; pp. 111 - 141 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
28.08.2006
|
| Online Access | Get full text |
| ISSN | 0550-3213 1873-1562 |
| DOI | 10.1016/j.nuclphysb.2006.05.008 |
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| Abstract | We present evidence that there is a non-trivial fixed point for the
AdS
D
+
1
non-linear sigma model in two dimensions, without any matter fields or additional couplings beyond the standard quadratic action subject to a quadratic constraint. A zero of the beta function, both in the bosonic and supersymmetric cases, appears to arise from competition between one-loop and higher loop effects. A string vacuum based on such a fixed point would have string scale curvature. The evidence presented is based on fixed-order calculations carried to four loops (corresponding to
O
(
α
′
3
)
in the spacetime effective action) and on large
D calculations carried to
O
(
D
−2
)
(but to all orders in
α
′
). We discuss ways in which the evidence might be misleading, and we discuss some features of the putative fixed point, including the central charge and an operator of negative dimension. We speculate that an approximately
AdS
5
version of this construction may provide a holographic dual for pure Yang–Mills theory, and that quotients of an
AdS
3
version might stand in for Calabi–Yau manifolds in compactifications to four dimensions. |
|---|---|
| AbstractList | We present evidence that there is a non-trivial fixed point for the
AdS
D
+
1
non-linear sigma model in two dimensions, without any matter fields or additional couplings beyond the standard quadratic action subject to a quadratic constraint. A zero of the beta function, both in the bosonic and supersymmetric cases, appears to arise from competition between one-loop and higher loop effects. A string vacuum based on such a fixed point would have string scale curvature. The evidence presented is based on fixed-order calculations carried to four loops (corresponding to
O
(
α
′
3
)
in the spacetime effective action) and on large
D calculations carried to
O
(
D
−2
)
(but to all orders in
α
′
). We discuss ways in which the evidence might be misleading, and we discuss some features of the putative fixed point, including the central charge and an operator of negative dimension. We speculate that an approximately
AdS
5
version of this construction may provide a holographic dual for pure Yang–Mills theory, and that quotients of an
AdS
3
version might stand in for Calabi–Yau manifolds in compactifications to four dimensions. |
| Author | Gubser, Steven S. Friess, Joshua J. |
| Author_xml | – sequence: 1 givenname: Joshua J. surname: Friess fullname: Friess, Joshua J. email: jfriess@princeton.edu – sequence: 2 givenname: Steven S. surname: Gubser fullname: Gubser, Steven S. |
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| CitedBy_id | crossref_primary_10_1103_RevModPhys_92_045005 crossref_primary_10_1103_PhysRevD_103_025016 crossref_primary_10_1140_epjc_s10052_019_7190_9 crossref_primary_10_21468_SciPostPhys_9_2_019 crossref_primary_10_1016_j_nuclphysb_2006_08_026 crossref_primary_10_1016_j_nuclphysb_2015_01_024 crossref_primary_10_1088_0264_9381_26_3_035023 crossref_primary_10_1088_1126_6708_2007_11_016 crossref_primary_10_1007_JHEP10_2011_047 crossref_primary_10_1007_JHEP01_2019_002 crossref_primary_10_1016_j_nuclphysb_2007_05_028 crossref_primary_10_1007_JHEP06_2016_145 crossref_primary_10_1088_1126_6708_2007_02_037 |
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