General relativity from string theory

In summary, this statement is that string theory implies general relativity i.e Einstein's field equations in some kind of a classical limit. This is done in almost all the textbooks out there, in particular GSW.
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  • #72
oh come on ricci flatness is hardly deep if you didn't have it then you'd violate energy conservation.
 
  • #73
Haelfix said:
Hi Nrqed, that is a truly excellent question and way above the level of Tong.

(for the identical statement said slightly differently, see Polchinksi):
http://books.google.com/books?id=k4...age&q=coherent states vertex operator&f=false

I think the answer to your first question is almost but not quite. The problem is there are gauge fixing ambiguities creeping into the calculation, and you have to ensure the symmetries of string theory (Virasoro constraints) are enforced. Consequently the naive definition of a coherent state must be slightly generalized to ensure this.

But once that is done, then yes there is a sense in which you can show that what you get is an eigenstate of the annihilation operator, although the paper I am looking at is technically challenging...

See
http://arxiv.org/abs/0911.5354v2 starting on page 27 for a discussion and the calculation for eg closed strings in lightcone gauge is on page 36, although the vertex operators are more general (DDF vertex operators). Maybe one of the stringy experts here knows a simpler calculation, but I have never seen it done nor could I find it in a quick literature search. I am actually a little surprised that I couldn't find the calculation done in texts regarding nonminimal sigma models, since this is very much isomorphic.

Thank you Haelfix, I truly appreciate your explanations. I will look at the references with great interest.
 
<h2>1. What is the relationship between general relativity and string theory?</h2><p>General relativity and string theory are both theories of physics that attempt to explain the fundamental workings of the universe. General relativity is a theory of gravity and space-time, while string theory is a theory of particles and their interactions. String theory is often seen as a more fundamental and comprehensive theory, which incorporates general relativity as a special case.</p><h2>2. How does string theory attempt to reconcile quantum mechanics and general relativity?</h2><p>One of the main goals of string theory is to unify the two main theories of physics, quantum mechanics and general relativity. General relativity describes the force of gravity on a large scale, while quantum mechanics explains the behavior of particles on a small scale. String theory proposes that all particles are actually tiny strings, and the interactions between these strings can explain both gravity and quantum mechanics.</p><h2>3. What are the implications of string theory for the concept of space-time?</h2><p>One of the key implications of string theory is that it suggests space-time is not a smooth, continuous fabric as described by general relativity, but rather a discrete and quantized structure. This means that at a very small scale, space and time are made up of tiny, indivisible units, rather than being infinitely divisible as described by general relativity.</p><h2>4. How does string theory explain the existence of multiple dimensions?</h2><p>String theory proposes that there are more than the three dimensions of space and one dimension of time that we experience in our daily lives. In fact, string theory predicts that there are 10 dimensions in total, with 6 of them being hidden from our perception. These extra dimensions are thought to be curled up and compactified, and their existence is necessary for the mathematical consistency of string theory.</p><h2>5. What evidence supports the validity of string theory?</h2><p>Currently, there is no direct experimental evidence for string theory, as the energies required to test it are far beyond our current technological capabilities. However, string theory has been successful in resolving some mathematical inconsistencies in other theories, and it has provided potential solutions for long-standing problems in physics, such as the unification of gravity and quantum mechanics. Additionally, some aspects of string theory have been indirectly supported by observations in cosmology, such as the existence of dark energy.</p>

1. What is the relationship between general relativity and string theory?

General relativity and string theory are both theories of physics that attempt to explain the fundamental workings of the universe. General relativity is a theory of gravity and space-time, while string theory is a theory of particles and their interactions. String theory is often seen as a more fundamental and comprehensive theory, which incorporates general relativity as a special case.

2. How does string theory attempt to reconcile quantum mechanics and general relativity?

One of the main goals of string theory is to unify the two main theories of physics, quantum mechanics and general relativity. General relativity describes the force of gravity on a large scale, while quantum mechanics explains the behavior of particles on a small scale. String theory proposes that all particles are actually tiny strings, and the interactions between these strings can explain both gravity and quantum mechanics.

3. What are the implications of string theory for the concept of space-time?

One of the key implications of string theory is that it suggests space-time is not a smooth, continuous fabric as described by general relativity, but rather a discrete and quantized structure. This means that at a very small scale, space and time are made up of tiny, indivisible units, rather than being infinitely divisible as described by general relativity.

4. How does string theory explain the existence of multiple dimensions?

String theory proposes that there are more than the three dimensions of space and one dimension of time that we experience in our daily lives. In fact, string theory predicts that there are 10 dimensions in total, with 6 of them being hidden from our perception. These extra dimensions are thought to be curled up and compactified, and their existence is necessary for the mathematical consistency of string theory.

5. What evidence supports the validity of string theory?

Currently, there is no direct experimental evidence for string theory, as the energies required to test it are far beyond our current technological capabilities. However, string theory has been successful in resolving some mathematical inconsistencies in other theories, and it has provided potential solutions for long-standing problems in physics, such as the unification of gravity and quantum mechanics. Additionally, some aspects of string theory have been indirectly supported by observations in cosmology, such as the existence of dark energy.

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