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.

scholarly journals PERTURBATIVE QUANTUM GAUGE FIELDS ON THE NONCOMMUTATIVE TORUS

2000 ◽  
Vol 15 (07) ◽  
pp. 1011-1029 ◽  
Author(s):  
THOMAS KRAJEWSKI ◽  
RAIMAR WULKENHAAR
Keyword(s):  
Gauge Fields ◽  
Infrared Singularity ◽  
Noncommutative Torus ◽  
Yang Mills ◽  
Free Theory ◽  
Feynman Rules ◽  
Perturbative Quantum ◽  
The One ◽  
Brs Symmetry ◽  
Invariant Regularization

Using standard field theoretical techniques, we survey pure Yang–Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry. Although in general free of any infrared singularity, the theory is ultraviolet divergent. Because of an invariant regularization scheme, this theory turns out to be renormalizable and the detailed computation of the one-loop counterterms is given, leading to an asymptotically free theory. Besides, it turns out that nonplanar diagrams are overall convergent when θ is irrational.

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.

PROBING MALDACENA–NUNEZ IN IR WITH p$\overline{\rm D3}$-BRANES

2004 ◽  
Vol 19 (26) ◽  
pp. 4517-4531
Author(s):  
SHESANSU SEKHAR PAL
Keyword(s):  
Radial Direction ◽  
Point Of View ◽  
Leading Order ◽  
Small Fluctuation ◽  
World Volume ◽  
The World ◽  
Dual Analysis

We probed Maldacena–Nunez solution in IR with p coincident anti-D3-branes and found that these probe branes become a fuzzy NS5-brane. Doing the dual analysis, i.e. from the NS5-brane point of view with the charge of p anti-D3-brane on the world-volume of NS5-brane, we showed that to leading order this potential matches with that of p anti-D3-branes and the potential on the NS5-brane has a stable minima and have also calculated the potential, from the NS5-brane point of view, for a small fluctuation along the radial direction.

scholarly journals INTERPRETING THE M2-BRANE ACTION

2009 ◽  
Vol 24 (10) ◽  
pp. 721-724 ◽  
Author(s):  
SHAMIK BANERJEE ◽  
ASHOKE SEN
Keyword(s):  
Scalar Field ◽  
Azimuthal Angle ◽  
Free Field ◽  
Brane World ◽  
Polar Coordinate System ◽  
Radial Coordinate ◽  
Field Equations ◽  
Yang Mills ◽  
World Volume ◽  
The World

The world-volume theory of multiple M2-branes proposed recently has a free scalar field. For large vev of this scalar field the world-volume action reduces to that of multiple D2-branes with Yang–Mills coupling proportional to the vev. We suggest that the correct interpretation of this scalar field is as the radial position of the M2-brane center of mass in a cylindrical polar coordinate system. Regarding the azimuthal angle as compact we can regard this as a set of coincident D2-branes in type IIA string theory with varying dilaton and metric. We find that the effective world-volume theory on the D2-branes has Yang–Mills coupling proportional to the radial coordinate; furthermore the radial coordinate satisfies free field equations of motion. This agrees with the corresponding results derived from the M2-brane world-volume theory.

scholarly journals Dirichlet to Neumann operator for Abelian Yang–Mills gauge fields

2017 ◽  
Vol 14 (11) ◽  
pp. 1750153
Author(s):  
Homero G. Díaz-Marín
Keyword(s):  
Boundary Conditions ◽  
Smooth Boundary ◽  
Complex Structure ◽  
Geometric Quantization ◽  
Symplectic Space ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Neumann Operator ◽  
Yang Mills ◽  
Dirichlet To Neumann Operator

We consider the Dirichlet to Neumann operator for Abelian Yang–Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler–Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.

scholarly journals FIELD STRENGTH FORMULATION OF SU(2) YANG–MILLS THEORY IN THE MAXIMAL ABELIAN GAUGE: PERTURBATION THEORY

1998 ◽  
Vol 13 (23) ◽  
pp. 4049-4076 ◽  
Author(s):  
M. QUANDT ◽  
H. REINHARDT
Keyword(s):  
Perturbation Theory ◽  
Gauge Field ◽  
Trivial Solution ◽  
Semiclassical Approximation ◽  
Tensor Fields ◽  
Abelian Gauge ◽  
Standard Result ◽  
Yang Mills ◽  
Β Function ◽  
The One

We present a reformulation of SU(2) Yang–Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a semiclassical approximation and the corresponding saddle point equation is derived. Besides the nontrivial solutions, which are presumably related to nonperturbative interactions for the Abelian gauge field, the equation of motion for the tensor fields allows for a trivial solution as well. We show that the semiclassical expansion around this trivial solution is equivalent to the standard perturbation theory. In particular, we calculate the one-loop β-function for the running coupling constant in this approach and reproduce the standard result.

LOCALIZATION OF NONLOCAL LAGRANGIANS AND MASS GENERATION FOR NON-ABELIAN GAUGE FIELDS

2008 ◽  
Vol 23 (26) ◽  
pp. 4289-4313
Author(s):  
ALEXEY SEVOSTYANOV
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Fields ◽  
Green Functions ◽  
Coupling Constant ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Three Dimensional Space

We introduce and study the four-dimensional analogue of a mass generation mechanism for non-Abelian gauge fields suggested in the paper, Phys. Lett. B403, 297 (1997), in the case of three-dimensional space–time. The construction of the corresponding quantized theory is based on the fact that some nonlocal actions may generate local expressions for Green functions. An example of such a theory is the ordinary Yang–Mills field where the contribution of the Faddeev–Popov determinant to the Green functions can be made local by introducing additional ghost fields. We show that the quantized Hamiltonian for our theory unitarily acts in a Hilbert space of states and prove that the theory is renormalizable to all orders of perturbation theory. One-loop coupling constant and mass renormalizations are also calculated.

SOLUTIONS TO YANG–MILLS EQUATIONS: QUASI-INSTANTONS, QUASI-MONOPOLES AND QUASI-VORTICES

1992 ◽  
Vol 07 (02) ◽  
pp. 269-285 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Lie Groups ◽  
Sigma Model ◽  
String Model ◽  
Gauge Fields ◽  
Relativistic String ◽  
Yang Mills ◽  
Self Duality ◽  
Model Equations ◽  
The One ◽  
Real Forms

Yang–Mills equations for semisimple gauge Lie groups G in d = 4 spaces with signatures (+ + + +) and (+ + − −) are considered. Generalizations of the one-monopole and one-instanton solutions to these equations for the group [Formula: see text] and for its real forms are obtained. For gauge fields of the vortex type, the Ansätze permitting the reduction of d = 4 self-duality equations to the d = 2 Liouville, sinh–Gordon and sine–Gordon, G/H sigma-model equations and to the equations of the relativistic string model are presented.

scholarly journals MASSIVE YANG–MILLS THEORY IN ABELIAN GAUGES

2003 ◽  
Vol 18 (09) ◽  
pp. 1595-1612 ◽  
Author(s):  
ULRICH ELLWANGER ◽  
NICOLÁS WSCHEBOR
Keyword(s):  
Standard Form ◽  
Gauge Fields ◽  
Wave Function Renormalization ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Renormalization Group Equations ◽  
Infrared Limit ◽  
Mass Terms ◽  
Renormalization Constants ◽  
Slavnov Taylor Identities

We prove the perturbative renormalizability of pure SU(2) Yang–Mills theory in the Abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow us to preserve the standard form of the Slavnov–Taylor identities (but with modified BRST variations), mass terms for the diagonal gauge fields require the study of modified Slavnov–Taylor identities. We comment on the renormalization group equations, which describe the variation of the effective action with the different masses. Finite renormalized masses for the charged gauge fields, in the limit of vanishing bare mass terms, are possible provided a certain combination of wave function renormalization constants vanishes sufficiently rapidly in the infrared limit.

scholarly journals TWO-LOOP GHOST–ANTIGHOST CONDENSATION FOR SU(2) YANG–MILLS THEORIES IN THE MAXIMAL ABELIAN GAUGE

2005 ◽  
Vol 20 (08) ◽  
pp. 585-596 ◽  
Author(s):  
A. R. FAZIO
Keyword(s):  
Effective Potential ◽  
Tree Level ◽  
Abelian Gauge ◽  
Yang Mills ◽  
The One

In the framework of the formalism of Cornwall et al. for composite operators, we study the ghost–antighost condensation in SU (2) Yang–Mills theories quantized in the maximal Abelian gauge and derive analytically a condensating effective potential at two ghost loops. We find that in this approximation the one-loop pairing ghost–antighost is not destroyed but no mass is generated if the ansatz for the propagator suggested by the tree level Hubbard–Stratonovich transformations is used.

Sign in / Sign up

Export Citation Format

Share Document