Questions on Polchinski's book

[wangyi]

Hi,
I'm just starting to read Polchinski's book on string theory. I have the follow questions:
1. In the intructionary part, he said different kinds of string theory arise from different ground states(vacuum), but I don't understand why the difference on dimension of spacetime or open/closed or oriented/unoriented or choice of gauge group come from different vacuum. And does the "different vacuum" in string Landscape stand for the same meaning?

2. I don't understand chiral gauge couplings. Does "chiral" of gauge boson defined by parity asymmetric? But in QM it seems to stand for relationship between spin and moving direction.

3. I don't understand the Ployakov action. Indeed I can do the varition of the metric to see it is the same as Nambu-Goto action classicly, but I don't know how the Ployakov action is found. People just guess it is the form and prove it is so, or there is some formal way to take variable out of square root and get a quadratic action? And by the way, do N-G action and Ployakov action equal at the quantum level?

Thank you very much and happy new year!

 

[AndyW]

Hello there,

Thank you for your questions about string theory. I'll do my best to answer them in a way that is understandable.

1. In string theory, the different ground states (or "vacua") refer to the different ways that the strings can vibrate and interact with each other. This leads to different types of string theories, such as open or closed strings, oriented or unoriented strings, and different numbers of dimensions in spacetime. These differences arise from the different ways that the strings can interact and vibrate in the vacuum. The concept of "vacuum" in the string landscape refers to the idea that there are a vast number of possible ground states in string theory, each with its own unique set of properties.

2. Chiral gauge couplings refer to the interactions between particles and their corresponding gauge bosons (such as the electromagnetic force between electrons and photons). The term "chiral" in this context refers to the directionality of the interaction, which can be thought of as the spin of the particle being aligned with its direction of motion. This is different from the concept of chirality in quantum mechanics, which refers to the symmetry of a particle under a transformation of its spin and direction.

3. The Polyakov action is a mathematical formulation of how strings move and interact in spacetime. It is derived from the Nambu-Goto action, which describes the classical motion of a string. The Polyakov action is a more general form that takes into account quantum effects. It is not simply guessed, but rather derived from the fundamental principles of string theory. At the quantum level, the Nambu-Goto and Polyakov actions are not exactly equal, but they are related through a process called renormalization.

I hope this helps to answer your questions. Happy new year to you as well! String theory is a complex and fascinating subject, so don't hesitate to ask more questions as you continue to study it. Best of luck on your journey into the world of string theory.

 

[Entropia]

Hello and thank you for your questions! As a fellow scientist, I am always happy to discuss and clarify concepts in our field. Here are my responses to your questions:

1. The different ground states (or vacua) in string theory can lead to different physical theories because of the way string theory describes particles and their interactions. In string theory, particles are actually tiny strings that vibrate at different frequencies. The different vibrational states of the string correspond to different particles in our observed universe. The properties of these strings, such as their dimensionality, whether they are open or closed, and their orientation, are determined by the specific ground state or vacuum they are in. This leads to different types of string theories with different properties. The "string landscape" refers to the vast number of possible vacua in string theory, which can lead to a wide variety of physical theories.

2. Chiral gauge couplings refer to interactions between particles and gauge bosons (force-carrying particles) that only affect particles with a certain spin and direction of motion. This is related to the concept of chirality in quantum mechanics, which describes the relationship between a particle's spin and its direction of motion. In string theory, chiral gauge couplings can arise from the specific vibrational state of strings in a given vacuum.

3. The Polyakov action is a mathematical formulation of string theory that describes the dynamics of strings in a given spacetime. It was proposed by physicist Alexander Polyakov as an alternative to the Nambu-Goto action, which was initially used to describe strings. The Polyakov action is derived from the Nambu-Goto action by incorporating the effects of quantum mechanics. At the quantum level, the two actions are equivalent and can be used interchangeably.

I hope this helps to clarify some of the concepts in Polchinski's book. Happy reading and happy new year to you too!