scholarly journals THE WALL OF THE CAVE

1999 ◽  
Vol 14 (05) ◽  
pp. 645-657 ◽  
Author(s):  
A. M. POLYAKOV
Keyword(s):  
Physical Meaning ◽  
Gauge Fields ◽  
Renormalization Scale ◽  
40Th Anniversary ◽  
World Sheet ◽  
Curved Space ◽  
Yang Mills ◽  
Fifth Dimension ◽  
The World ◽  
Noncritical Strings

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang–Mills theories must be described by the noncritical strings in the five-dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang–Mills theories. The article is written on the occasion of the 40th anniversary of the IHES.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645040
Author(s):  
Arkady Vainshtein
Keyword(s):  
Sigma Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
World Sheet ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Straightforward Method ◽  
The World ◽  
Original Formula

We study two-dimensional sigma models where the chiral deformation diminished the original [Formula: see text] supersymmetry to the chiral one, [Formula: see text]. Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional [Formula: see text] theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the [Formula: see text] functions in terms of the anomalous dimensions analogous to the NSVZ [Formula: see text] function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

scholarly journals Holographic baryons and instanton crystals

2015 ◽  
Vol 29 (16) ◽  
pp. 1540052 ◽  
Author(s):  
Vadim Kaplunovsky ◽  
Dmitry Melnikov ◽  
Jacob Sonnenschein
Keyword(s):  
Gauge Fields ◽  
Leading Order ◽  
Abelian Gauge ◽  
Yang Mills ◽  
World Volume ◽  
Dense Nuclear Matter ◽  
The World ◽  
The One ◽  
Holographic Description ◽  
Matter Phase

In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-Abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang–Mills instantons, whose solutions can be constructed from the celebrated Atiyah–Drinfeld–Hitchin–Manin (ADHM) construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review, we summarize the known results on the construction and phases of crystals of the holographic baryons.

INDEX THEOREM AND CHIRAL ANOMALY IN D = 4, N = 1 SUPERGRAVITY

1990 ◽  
Vol 05 (14) ◽  
pp. 1097-1102 ◽  
Author(s):  
SATOSHI YAJIMA
Keyword(s):  
Index Theorem ◽  
Flat Space ◽  
Integral Approach ◽  
Chiral Anomaly ◽  
Gauge Fields ◽  
Minimal Coupling ◽  
Curved Space ◽  
Yang Mills ◽  
Anomalous Term ◽  
Fermion Fields

The chiral anomaly in D = 4 supergravity coupled to supersymmetric Yang-Mills theory is evaluated by using the path integral approach. We consider not only the minimal coupling between the gravitational and gauge fields and the fermion fields but also the interaction term which mixes the gravitino and gaugino. The explicit form of the new anomalous term is given by rewriting the resultant term obtained in flat space in a form corresponding to curved space.

CONSISTENCY CONDITION FOR κ-ANOMALIES AND SUPERSPACE CONSTRAINTS IN QUANTUM HETEROTIC SUPERSTRINGS

1989 ◽  
Vol 04 (08) ◽  
pp. 1983-2013 ◽  
Author(s):  
M. TONIN
Keyword(s):  
General Structure ◽  
Consistency Condition ◽  
Quantum Corrections ◽  
World Sheet ◽  
Yang Mills ◽  
The World

In this paper, the quantum heterotic Green and Schwarz superstring in Yang-Mills and curved superspace background is investigated. A consistency condition for the anomalies, allowing to study their general structure, has been obtained. We have found that the anomalies of the κ-symmetry can be absorbed by consistent quantum corrections of torsion and curvatures leading to superspace constraints in agreement with those considered in recent studies on SUGRA-SYM models. Moreover we suggest that the world sheet conformal and Lorentz anomalies vanish if the κ-anomalies are cancelled.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Stress-energy tensor correlators from the world-sheet

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hanno Bertle ◽  
Andrea Dei ◽  
Matthias R. Gaberdiel
Keyword(s):  
Vertex Operator ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
World Sheet ◽  
Stress Energy ◽  
The World

Abstract The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.

Sign in / Sign up

Export Citation Format

Share Document