scholarly journals A Deconstruction Lattice Description of the D1/D5 Brane World-Volume Gauge Theory

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Joel Giedt
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Lattice Theory ◽  
Lattice Structure ◽  
Brane World ◽  
Two Dimensional ◽  
Fermi Statistics ◽  
World Volume ◽  
Infrared Limit

I generalize the deconstruction lattice formulation of Endres and Kaplan to two-dimensional super-QCD with eight supercharges, denoted by (4,4), and bifundamental matter. I specialize to a particularly interesting (4,4) gauge theory, with gauge groupU(Nc)×U(Nf), andU(Nf)being weakly gauged. It describes the infrared limit of the D1/D5 brane system, which has been studied extensively as an example of the AdS3/CFT2correspondence. The construction here preserves two supercharges exactly and has a lattice structure quite similar to that which has previously appeared in the deconstruction approach, that is, site, link, and diagonal fields with both the Bose and Fermi statistics. I remark on possible applications of the lattice theory that would test the AdS3/CFT2correspondence, particularly one that would exploit the recent worldsheet instanton analysis of Chen and Tong.

scholarly journals Two dimensional super QCD on a lattice

2018 ◽  
Vol 175 ◽  
pp. 08005
Author(s):  
Simon Catterall ◽  
Aarti Veernala
Keyword(s):  
Numerical Simulations ◽  
Gauge Group ◽  
Lattice Theory ◽  
Scalar Potential ◽  
Flavor Symmetry ◽  
Theoretical Expectation ◽  
Two Dimensional ◽  
Fundamental Representation ◽  
Lattice Action

We construct a lattice theory with one exact supersymmetry which consists of fields transforming in both the adjoint and fundamental representations of a U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf flavors of fermion in the fundamental representation along with their scalar partners and is invariant under a global U(Nf) flavor symmetry. The lattice action contains an additional Fayet-Iliopoulos term which can be used to generate a scalar potential. We perform numerical simulations that corroborate the theoretical expectation that supersymmetry is spontaneously broken for Nf<Nc.

scholarly journals Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Mendel Nguyen ◽  
Yuya Tanizaki ◽  
Mithat Ünsal
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Lattice Theory ◽  
Lattice Gauge Theory ◽  
Global Symmetry ◽  
Leading Order ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Lattice Gauge ◽  
Abelian Lattice

Abstract We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.

LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS

1990 ◽  
Vol 05 (09) ◽  
pp. 693-703 ◽  
Author(s):  
B. YE. RUSAKOV
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Point Of View ◽  
Irreducible Representations ◽  
Partition Functions ◽  
Two Dimensional ◽  
Geometrical Characteristics ◽  
Physical Quantities

Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including nonorientable ones. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities’ point of view, non-orientability of the manifold is equivalent to its non-compactness.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Mocking the u-plane integral

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Georgios Korpas ◽  
Jan Manschot ◽  
Gregory W. Moore ◽  
Iurii Nidaiev
Keyword(s):  
Asymptotic Behavior ◽  
Gauge Theory ◽  
Entire Function ◽  
Gauge Group ◽  
Strong Coupling ◽  
Modular Forms ◽  
Correlation Functions ◽  
Coulomb Branch ◽  
Mock Modular Forms ◽  
Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

scholarly journals META-STABLE BRANE CONFIGURATIONS WITH MULTIPLE NS5-BRANES

2009 ◽  
Vol 24 (27) ◽  
pp. 5051-5120
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
The Other ◽  
Multiple Product

Starting from an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group and the bifundamentals, we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. Then we describe the intersecting brane configurations, where there are NS-branes and D4-branes (and anti-D4-branes), of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where the orientifold 4-planes are added into the above brane configuration. Next, by adding an orientifold 6-plane, we apply to an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group (where a single symplectic or orthogonal gauge group is present) and the bifundamentals. Finally, we describe the other cases where the orientifold 6-plane intersects with NS-brane.

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

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