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Jack2013
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Can somebody clarify how the formula for variation of the auxilliary worldsheet metric is obtained due to reparametrization of the worldsheet in string theory??
The auxiliary worldsheet metric is a mathematical tool used in string theory to describe the geometry of the two-dimensional surface (known as the worldsheet) that a string traces out as it moves through spacetime. It is a complex metric that includes both the physical metric of the spacetime and additional terms that account for the quantum fluctuations of the string.
The variation of the auxiliary worldsheet metric is important because it allows us to study the dynamics of strings in a curved spacetime. By varying the metric, we can understand how the shape of the worldsheet changes as the string moves through different regions of spacetime, providing insights into the behavior of strings in curved backgrounds.
The variation of the auxiliary worldsheet metric is calculated using a mathematical technique called functional derivatives. This involves taking the derivative of the action (mathematical expression that describes the dynamics of the system) with respect to the metric, and then solving the resulting equations of motion.
The variation of the auxiliary worldsheet metric is crucial in string theory because it allows us to incorporate quantum effects into the theory. By considering the fluctuations of the string's worldsheet, we can better understand the behavior of strings in curved spacetime and potentially resolve some of the outstanding problems in theoretical physics, such as the reconciliation of general relativity and quantum mechanics.
The variation of the auxiliary worldsheet metric is closely related to other concepts in string theory, such as the stress-energy tensor and the conformal field theory. These concepts are all interconnected and together provide a comprehensive understanding of the dynamics of strings in curved spacetime. The variation of the auxiliary worldsheet metric is a crucial component in this framework, allowing for a deeper understanding of the behavior of strings in different backgrounds.