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Quantum Fields and Strings Group Seminar
From closed to open strings: the tensionless route in Kalb–Ramond background and noncommutativity
From closed to open strings: the tensionless route in Kalb–Ramond background and noncommutativity
演讲者
Sarthak Duary
时间
2025年12月18日 15:00 至 16:30
地点
A7-302
线上
Zoom 388 528 9728
(BIMSA)
摘要
In this talk, I will present tensionless bosonic strings in a constant Kalb–Ramond background. I will show how the tensionless (Carrollian) limit induces a universal gluing between worldsheet oscillators, how this gluing generalizes in the presence of a constant (B)-field, and how the resulting mixed boundary conditions lead to a gluing matrix and a generalized induced vacuum that appears as a squeezed boundary state. This vacuum emerges continuously from the closed-string vacuum through a Bogoliubov transformation, giving an explicit realization of the closed-to-open string transition. I will also comment on toroidal compactifications, where the mechanism of worldsheet Bose–Einstein condensation remains unchanged.
I will then turn to the second goal of the work: understanding the noncommutative picture for tensionless strings. In the tensionless regime, the worldsheet metric becomes degenerate. Because of this, the standard Seiberg–Witten operator approach based on evaluating the open-string two-point function cannot be applied. Instead, I will use the symplectic formalism, which works directly with the boundary phase space. In this framework, the key object is the boundary symplectic two-form, obtained from the first-order part of the action. The structure of this two-form fixes the canonical brackets: its inverse determines the equal-time Poisson brackets of the boundary coordinates. Upon quantization, these Poisson brackets become commutators, and the coefficient of the delta function thus gives the noncommutative parameter. I will show that both tensile and tensionless strings can be treated uniformly in this symplectic language. In the tensile case, the metric and B-field together produce the boundary symplectic two-form whose inverse gives the Seiberg–Witten noncommutativity parameter. In the tensionless case, the B-field term gives the boundary symplectic form. Thus, tensionless strings realize a Seiberg–Witten type noncommutativity as an intrinsic feature.
I will then turn to the second goal of the work: understanding the noncommutative picture for tensionless strings. In the tensionless regime, the worldsheet metric becomes degenerate. Because of this, the standard Seiberg–Witten operator approach based on evaluating the open-string two-point function cannot be applied. Instead, I will use the symplectic formalism, which works directly with the boundary phase space. In this framework, the key object is the boundary symplectic two-form, obtained from the first-order part of the action. The structure of this two-form fixes the canonical brackets: its inverse determines the equal-time Poisson brackets of the boundary coordinates. Upon quantization, these Poisson brackets become commutators, and the coefficient of the delta function thus gives the noncommutative parameter. I will show that both tensile and tensionless strings can be treated uniformly in this symplectic language. In the tensile case, the metric and B-field together produce the boundary symplectic two-form whose inverse gives the Seiberg–Witten noncommutativity parameter. In the tensionless case, the B-field term gives the boundary symplectic form. Thus, tensionless strings realize a Seiberg–Witten type noncommutativity as an intrinsic feature.