Conformally gauge-fixed Polyakov D1-brane action in the presence of a 2-form gauge field: the instant-form and front-form Hamiltonian and path integral formulations

Kulshreshtha, Usha; Kulshreshtha, Daya Shankar

doi:10.1016/s0370-2693(03)00056-x

Cited by 30 publications

(139 citation statements)

References 12 publications

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“…Conformally gauge-fixed Polyakov D1 brane action [1,2] is quantized on the light-front using the equal light-cone (LC) world-sheet (WS) time framework on the hyperplanes of the LF defined by the LC-WS time σ + = (τ + σ ) = constant. The Polyakov D1 brane action which describes the propagation of a D1 brane in a d-dimensional curved background h αβ (with d = 10 for the fermionic and d = 26 for bosonic D1 brane) is defined by [1,2]:…”

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

“…The Polyakov D1 brane action which describes the propagation of a D1 brane in a d-dimensional curved background h αβ (with d = 10 for the fermionic and d = 26 for bosonic D1 brane) is defined by [1,2]:…”

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

“…Also because the metric components h αβ are varied in the above equation, the 2-dimensional gravitational field h αβ is treated not as a given background field, but rather as an adjustable quantity coupled to the scalar fields [1]. The actionS has the well-known three local gauge symmetries given by the 2-dimensional WS reparametrization invariance (WSRI) and the Weyl invariance (WI) [1,2]. We could use the three local gauge symmeties of the theory to choose h αβ to be of a particular form [1,2]:…”

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

“…The actionS has the well-known three local gauge symmetries given by the 2-dimensional WS reparametrization invariance (WSRI) and the Weyl invariance (WI) [1,2]. We could use the three local gauge symmeties of the theory to choose h αβ to be of a particular form [1,2]:…”

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

“…where the phase space variables of the theory are Φ k ≡ (X + , X − , X i , u, v, w i ) with the corresponding respective canonical conjugate momenta: [2,3]:…”

Section: Pos(lc2008)007mentioning

confidence: 99%

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Polyakov D1 brane action on the light-front

Kulshreshtha¹

2009

Proceedings of LIGHT CONE 2008 Relativistic Nuclear and Particle Physics — PoS(LC2008)

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Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

Section: Conformally Gauge-fixed Polyakov D1 Brane Actionmentioning

confidence: 99%

“…where the phase space variables of the theory are Φ k ≡ (X + , X − , X i , u, v, w i ) with the corresponding respective canonical conjugate momenta: [2,3]:…”

Section: Pos(lc2008)007mentioning

confidence: 99%

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Polyakov D1 brane action on the light-front

Kulshreshtha¹

2009

Proceedings of LIGHT CONE 2008 Relativistic Nuclear and Particle Physics — PoS(LC2008)

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Light-Front Quantization of the Chern–Simons–Higgs Theory in the Broken Symmetry Phase

Kulshreshtha

2011

Few-Body Syst

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Two-space one-time dimensional Chern-Simons-Higgs theory is quantized on the light-front in the broken (frozen) symmetry phase of the Higgs potential.Gauge theories in two-space one-time dimensions involving Chern-Simons (CS) term coupled to matter fields describe excitations with fractional statistics [1][2][3][4][5][6][7][8]. Such studies form a broad field of study [1][2][3][4][5][6][7][8]. Recently we have studied the instant-form (IF) quantization (IFQ) [6,7] of this theory in the presence of the Higgs potential (on the hyperplanes: x 0 = t = constant) in the so-called symmetry phase (SP) of the Higgs potential [6] as well as in the so-called broken (frozen) symmetry phase of the Higgs potential [7]. We have also studied the light-front (LF) quantization (LFQ) of this theory in the symmetry phase of the Higgs potential [8]. In the present work we study the light-front quantization (LFQ) of the theory in the broken (or frozen) symmetry phase of the Higgs potential where the phase ϕ(x μ ) of the complex matter field (x μ ) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone boson [4,7] under appropriate gauge-fixing using the Hamiltonian [9,10], path integral [10] and BRST [11] formulations using the light-front (LF) [12,13] dynamics (on the hyperplanes defined by the LC time: (τ ≡ x + = (x 0 +x 1 ) √ 2 = constant) [12,13]. The Chern-Simons-Higgs theory in two-space one-time dimensions is defined by the action [1-8]:g μν := diag(+1, −1, −1); μ, ν = 0, 1, 2; 012 = 012 = +1( 1 d )Here θ is the Chern-Simons parameter. The Higgs potential is kept rather general, without making any specific choice for the parameters of the potential except that they are chosen such that the potential remains a double well potential with 0 = 0. In the following, we study this theory in the so-called broken (or frozen) symmetry phase (BSP) [4,6], of the complex matter field [≡ (x μ )]. For this purpose, for the complex matter field we take [4,7]:

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Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

Kulshreshtha

2011

Few-Body Syst

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Light-front quantization of the conformally gauge-fixed Polyakov D1 brane action in the presence of a constant background scalar axion field C(τ, σ ) and an U (1) gauge field A α (τ, σ ) is studied. The axion field C and the U (1) gauge field A α , are seen to behave like the Wess-Zumino (WZ) fields and the term involving these fields is seen to behave like a WZ term for this action.The Polyakov action is one of the most widely studied topics in string theory [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Recently we have studied [9][10][11][12][13][14][15][16] the Hamiltonian [17] and path integral [9,[12][13][14][15][16] formulations of the conformally gauge-fixed Polyakov D1 brane action (CGFPD1BA) with and without a scalar dilaton field in the instant-form (IF) quantization (IFQ) [12,18,19] as well as in the light-front (LF) quantization (LFQ) [9,[13][14][15][16]18,19] (using the IF of dynamics [18,19] on the hyperplanes defined by the World-Sheet (WS) time σ 0 = τ = constant for IFQ [18,19] and using the light-front (LF) dynamics on the hyperplanes of the LF defined by the light-cone (LC) time: σ + = (τ + σ ) = constant) [18,19]. In both the above cases the theory is seen to be gauge-non-invariant(GNI) [9], [12][13][14][15][16], possessing a set of second-class constraints, owing to the conformal gauge-fixing of the theory. This GNI theory has been studied by us in Ref. [9] in the presence of a constant anti-symmetric 2-form gauge field B αβ (≡ B αβ (τ, σ )) which is a scalar field in the target space and an anti-symmetric field in the WS space. This 2-form gauge field B αβ in this case is seen to behave like a Wess-Zumino(WZ) field and the term involving this field in the action is seen to behave like a WZ term for the CGFPD1BA. The CGFPD1BA (being a conformally gauge-fixed theory) is GNI and it does not respect the usual string gauge symmetries defined by the WS reparametrization invariance (WSRI) and the Weyl invariance (WI) [1][2][3][4][5][6][7][8]. However, in the presence of a constant 2-form gauge field B αβ it is seen [9,12-16] to describe a gauge-inavriant (GI) theory respecting the usual string gauge symmetries defined by the WSRI and the WI.In the present work we study this CGFPD1BA in the presence of a constant background scalar axion field C(≡ C(τ, σ ))) an U (1) gauge field A α (≡ A α (τ, σ ))), where C is a constant scalar field in the target space as well as in the WS space and A α is a scalar field in the target space and a vector field in the WS space. We find that the resulting theory obtained in the above manner describes a GI system respecting the usual string gauge symmetries defined by the WSRI and the WI. It is seen that the axion field C and the U (1) gauge field A α , in the resulting theory behave like the WZ fields and the term involving these fields behaves like a WZ term for the CGFPD1BA. In the present work we study the LFQ of this GI theory describing the CGFPD1BA in the presence of the constant scalar axion field C and the U (1) gauge field A α under appropriate gau...

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Conformally gauge-fixed Polyakov D1-brane action in the presence of a 2-form gauge field: the instant-form and front-form Hamiltonian and path integral formulations

Cited by 30 publications

References 12 publications

Polyakov D1 brane action on the light-front

Polyakov D1 brane action on the light-front

Light-Front Quantization of the Chern–Simons–Higgs Theory in the Broken Symmetry Phase

Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

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