Approximate Bogomol’nyi-Prasad-Sommerfield States

Hiller, John R.; Pinsky, Stephen S.; Trittmann, Uwe

doi:10.1103/physrevlett.89.181602

Cited by 13 publications

(65 citation statements)

References 17 publications

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“…This freezes out the long, lower-mass states that characterize (1+1)-dimensional SYM theory. Interestingly, however, the massless BPS states become massive approximate BPS states and have masses that are nearly independent of the YM coupling [4], as seen in Fig. 1(a) where we show the two lowest Z 2 -even approximate BPS states have squared masses of 4κ 2 and 16κ 2 at infinite YM coupling.…”

Section: Setting the Stagementioning

confidence: 81%

“…At small g and low energy we recover the (1+1)-dimensional theory. At higher energy we find a series of Kaluza-Klein states, which we discuss in detail elsewhere [24]. At large coupling one might expect that the transverse Q − ⊥ /g term would freeze out, and one would see states that are a reflection of the (1+1)-dimensional theory.…”

Section: Setting the Stagementioning

confidence: 99%

“…This additional approximation allows us to carry the calculation to nine units of transverse resolution, T = 9, and nine units of longitudinal resolution, K = 9. The details of this analysis will be presented elsewhere [24]. At g = 0.5 we are unable to make this approximation and are only able to go to maximum resolutions of K = 6 and T = 4.…”

Section: Dlcq Analysismentioning

confidence: 99%

“…All the analysis of this sector goes through similarly to the Z 2 = +1 sector and will also be presented elsewhere [24].…”

Section: Dlcq Analysismentioning

confidence: 99%

“…N = 1 pure supersymmetric Yang-Mills (SYM) theory in 1+1 and 2+1 dimensions has massless BPS states [1,2]. Recently [3,4] we created an effective mass for the constituents of a SYM theory in 1+1 dimensions by adding a dimensionally reduced Chern-Simons (CS) term [5] to the theory. Although such a term does not break the supersymmetry, the theory with a CS term does not have BPS states.…”

Section: Introductionmentioning

confidence: 99%

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Anomalously light states in super-Yang–Mills–Chern–Simons theory

2002

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Inspired by our previous finding that supersymmetric Yang-Mills-ChernSimons (SYM-CS) theory dimensionally reduced to 1+1 dimensions possesses approximate Bogomol'nyi-Prasad-Sommerfield (BPS) states, we study the analogous phenomenon in the three-dimensional theory. Approximate BPS states in two dimensions have masses which are nearly independent of the Yang-Mills coupling and proportional to their average number of partons. These states are a reflection of the exactly massless BPS states of the underlying pure SYM theory. In three dimensions we find that this mechanism leads to anomalously light bound states. While the mass scale is still proportional to the average number of partons times the square of the CS coupling, the average number of partons in these bound states changes with the Yang-Mills coupling. Therefore, the masses of these states are not independent of the coupling. Our numerical calculations are done using supersymmetric discrete light-cone quantization (SDLCQ).

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Section: Setting the Stagementioning

confidence: 81%

Section: Setting the Stagementioning

confidence: 99%

Section: Dlcq Analysismentioning

confidence: 99%

“…All the analysis of this sector goes through similarly to the Z 2 = +1 sector and will also be presented elsewhere [24].…”

Section: Dlcq Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anomalously light states in super-Yang–Mills–Chern–Simons theory

2002

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Field Theory Correlators and String Theory

Pinsky

Trittmann

Hiller

The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Elementary Particle Physics

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It appears that string-M-theory is the only viable candidate for a complete theory of matter. It must therefore contain both gravity and QCD. What is particularly surprising is the recent conjecture that strongly coupled QCD matrix elements can be evaluated though a duality with weakly coupled gravity. To date there has been no direct verification of this conjecture by Maldacena because of the difficulty of direct strong coupling calculations in gauge theories. We report here on some progress in evaluating a gauge-invariant correlator in the non-perturbative regime in two and three dimensions in SYM theories. The calculations are made using supersymmetric discrete light-cone quantization (SDLCQ). We consider a Maldacena-type conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation, solve the corresponding N = (8, 8) SYM theory in two dimensions, and evaluate the correlator of the stress-energy tensor. Our numerical results support the Maldacena conjecture and are within 10-15% of the predicted results. We also present a calculation of the stress-energy correlator in N = 1 SYM theory in 2+1 dimensions. While there is no known duality relating this theory to supergravity, the theory does have massless BPS states, and the correlator gives important information about the BPS wave function in the non-perturbative regime.

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Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

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Approximate Bogomol’nyi-Prasad-Sommerfield States

Cited by 13 publications

References 17 publications

Anomalously light states in super-Yang–Mills–Chern–Simons theory

Anomalously light states in super-Yang–Mills–Chern–Simons theory

Field Theory Correlators and String Theory

Nonperturbative light-front Hamiltonian methods

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