A class of theories that attempt to explain all existing particles (including force carriers) as vibrational modes of extended objects, such as the 1-dimensional fundamental string. PLEASE DO NOT USE THIS TAG for non-relativistic material strings, such as, e.g., a guitar string.

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2
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2answers
160 views

How to find the rank of the matrix $\frac{\partial ^2\mathcal{L}}{\partial \dot{X^\mu} \partial \dot{X^\nu} }$ for the Nambu-Goto string Lagrangian?

In this case $$\mathcal{L}~=~-T\sqrt{-\dot{X^2}X'^2+(\dot{X}\cdot X')^2}.$$ I was reading some books and papers about the constraints in the Nambu-Goto action, and all of them say something like ...
2
votes
1answer
214 views

Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
5
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3answers
154 views

What happens at the center of a black hole according to holographic theory?

As far as I understand, the AdS/CFT correspondence proposed by Maldacena is an exact duality to a four-dimensional theory, which interpolates between one well-defined conformal field theory in the UV ...
0
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0answers
63 views

Ishibashi states and Cardy states in CFT

What are the Ishibashi states and Cardy states in CFTs? I am familiar with conformal field theory language. It would be great if someone can discuss about the basic idea of these states and their ...
5
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2answers
116 views

What laws are the same in all string theory compactifications?

In the string theory landscape, the set of particles we observe, their masses and interaction strengths originate from one of many different possible compactifications. What fundamental physical ...
2
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2answers
61 views

Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?

In these notes by Vafa on topological string theory he says in page 7 that the moduli of the 2-torus can be repackaged into two quantities: $$A=iR_1/R_2 \,\,\,\,\,\,\,\,\, \tau=iR_2/R_1$$ where $A$ ...
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1answer
188 views

Why are right hand neutrinos unaffected by all forces except gravity

I'm curious as to something I read on Berkeley's website. Does anyone happen to know why, according to this model,right hand neutrinos are unaffected by all forces except gravity? (Model taken from ...
6
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0answers
130 views

Monstrous Moonshine outside of String Theory

My question concerns applications of monstrous moonshine, which is the connection between the $j$-function and the monster group. Recently, physicists have applied it to string theory and, ultimately, ...
0
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0answers
28 views

Why are closed strings with different perioidicities equivalent?

I was typing up some lecture notes the other day when I saw something unclear. While talking about bosonic open and closed strings and the Polyakov action, the notes say we don't need to distinguish ...
4
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2answers
168 views

Traces in different representation

I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...
1
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1answer
81 views

Facing a problem in Katrin Becker, Melanie Becker, John Schwarz's String Theory

In BBS's string theory book, in the equation (2.143), it says that $$\text{tr} \omega ^N=\prod _{n=1}^{\infty } \left(\prod _{i=1}^{24} \text{tr} \omega ^{\alpha _{-n}^i \:\alpha _n^i}\right)=\prod ...
1
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1answer
69 views

Quark-gluon plasma: status [closed]

Can we say that a QGP has been observed or is there only suggestive evidence? Is the idea that string theory, through the AdS/CFT correspondence, could help to understand this new state of matter ...
4
votes
1answer
737 views

Conversion of the Polyakov action into the Nambo-Goto action?

I've read that the Polyakov action using an intrinsic metric $h_{\alpha\beta}$ $$\tag{1} S_P ~=~ -\frac{T}{2}\int d^2 \sigma \sqrt{-h}h^{\alpha\beta} \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu} ...
1
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1answer
70 views

Elementary question about global supersymmetry of a worldsheet [closed]

I'm reading chapter 4 of the book by Green, Schwarz and Witten. They consider an action $$ S = -\frac{1}{2\pi} \int d^2 \sigma \left( \partial_\alpha X^\mu \partial^\alpha X_\mu - i \bar \psi^\mu ...
1
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0answers
77 views

Branes at the conifold

Consider $N$ $D3$-branes at the singularity of the conifold. This particular example can be viewed as a $AdS_{5} \times T^{1,1}$ in the near horizon limit, where the Einstein manifold has isometry ...
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0answers
26 views

Polchinski equation 11.2.7

In Polchinski's string theory volume 2, when discussing the GSO projection for the heterotic string he says: In the IIA and IIB superstrings the GSO projection acted separately on the left- and ...
154
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11answers
22k views

What experiment would disprove string theory?

I know that there's big controversy between two groups of physicists: those who support string theory (most of them, I think) and those who oppose it. One of the arguments of the second group is ...
2
votes
1answer
118 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...
1
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1answer
184 views

Could M-Theory explain dark matter as well as dark energy?

Is it possible that M-Theory provides a solution to the mystery of dark matter and dark energy? The idea of dark matter and dark energy is that there is some inexplicable source affecting our ...
0
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0answers
17 views

Dirac Matrix property suitable to finding sets of intersecting branes

So, 11 dimensional supergravity has four oft-studied half-BPS states, the KK1 plane wave, the M2 brane, the M5 brane and the KK6 monopole. To figure out if we can find more solutions in the form of ...
1
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0answers
69 views

String theory book comparision : Polchinski and Blumenhagen,Lust & Theisen [closed]

I have studied Quantum Field Theory and General Relativity, and now wish to study string theory. I have gone through the book recommendation questions on this site (1, 2) which are very helpful. ...
0
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3answers
151 views

What is the general theory that describes the interactions between strings?

What is the general theory that describes the interactions between strings? I mean the basic object in the theory is (closed) string and they have interactions among them. The string theory, as I ...
0
votes
1answer
135 views

Polchinski Equation (7.2.4)

On page 209 of Polchinski's string theory book he writes down the expectation value of a product of vertex operators on the torus; equation $(7.2.4)$. The derivation is analogous to an earlier ...
2
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1answer
61 views

Standard derivation of Witt algebra

I have been studying Conformal field theory for the past one week from the books by Blumenhagen and Di Francesco etal. If I understand correctly, whenever one talks of 'local (infinitesimal) ...
1
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1answer
65 views

Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?

Quantum chromodynamics, or QCD, is the theory describing the strong nuclear force. Carried by gluons, it binds quarks into particles like protons and neutrons. According to the theory, the tiny ...
3
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0answers
144 views

Chiral Scale and Conformal Invariance in 2D QFT

I am reading a paper by Hofman and Strominger. In the appendix A, I have reproduced the equations (A10). Now they made a statement that "The Jacobi identity can be used to show that $O_h$ and $O_p$ ...
3
votes
0answers
115 views

Is there a Ramond vacuum for real fermions?

When studying the CFT of a complex fermion $\Psi$ we know that if it's periodic, ie if $$\Psi(\sigma_1+2\pi,\sigma_2)=\Psi(\sigma_1,\sigma_2)$$ then there is a doubly degenerate Ramond vacuum which I ...
6
votes
1answer
168 views

Why holographic renormalization?

Why is there a need to perform holographic renormalization for the normal $AdS_5\times S^5$/CFT$_4$ correspondence if the brane theory is conformal? Since the flow along the AdS direction $r$ is ...
1
vote
2answers
152 views

Elliptic genus; What is it within string/M-theory?

What is the elliptic genus (see also Witten index) in string/M-theory and (susy gauge)field theory constructions out of them? What does it tell us heuristically and what is its relation to the ...
0
votes
3answers
183 views

why does string theory require holography?

string theory solve the high energy gravity problem by making it mushier: Warped Passages - 14 - String Theory’s Origins Strings—unlike quarks—have no hard scattering processes. They have ...
3
votes
4answers
6k views

Why does string theory require 9 dimensions of space and one dimension of time?

String theorists say that there are many more dimensions out there, but they are too small to be detected. However, I do not understand why there are ten dimensions and not just any other number? ...
3
votes
2answers
279 views

Vertex operator and normal ordering

The two point function, or propagator for a free massless boson, $\phi$ in 2 dimensions is given by, $$\begin{equation} \langle \phi (z,\bar{z})\phi(w, \bar{w})\rangle ~=~ ...
1
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1answer
308 views

D-branes wrapping divisors and/or cycles

What is the difference between a divisor and a homology cycle? What is the difference between a D-brane wrapped around a divisor and a D-brane wrapped around a cycle?
3
votes
0answers
62 views

Branes wrapping curves in M-theory. What does it mean?

What does it mean that a M5-branes wraps a holomorphic curve in M-theory? In specific a lot of Vafa's paper involve various branes (not only M5) wrapping some cycles. What does this really mean ...
4
votes
2answers
116 views

Understanding the AdS/CFT Correspondence [duplicate]

I am beginning to learn about the AdS/CFT correspondence, but I can't find a comprehensive introduction that includes the relevant gravitational/string theory physics. What specific areas of general ...
0
votes
1answer
131 views

How do we know there are dimensions above the third?

Excluding the interpretation of time being the forth dimension, what mathematical evidence is there that suggests it exists? When talking about string theory they say how there is 12 dimensions and I ...
0
votes
1answer
83 views

Deriving the energy-momentum tensor conservation equation in complex coordinates, Polchinski 2.4.2

I am trying to derive equation (2.4.2) in Polchinski's string theory textbook, $$\overline \partial T_{zz}=\partial T_{\overline z \overline z} = 0 \tag{2.4.2}.$$ Using the conservation equation, ...
3
votes
1answer
289 views
1
vote
0answers
39 views

Need explanation for $CY_3$ folds comes first rather than algebraic curves comes first [duplicate]

The example I am aware of so far is quintic 3-fold equipped with $SU(3)$ holonomy. Why it is more natural to talk about $CY_3$ folds or Calibi-Yau 3 folds without talking about algebraic curves in ...
5
votes
1answer
172 views

Basic question about superspace, Grassmann numbers and world sheet supersymmetry

So, I'm trying to read the section on superspace from the book on string theory by Becker, Becker and Schwarz, and I realized that I've been stuck on something simple for a while. Some relevant ...
3
votes
0answers
71 views

A question about genus one string amplitude

In BCOV's paper http://arxiv.org/abs/hep-th/9309140 the genus one string amplitude of a Calabi-Yau 3-fold was explained in the B-model as the Ray-Singer torsion (there is a similar discussion in the ...
1
vote
0answers
49 views

Supersymmetries of the type IIB D3-brane action

The following query is based on a reading of section 2.2 of a paper by Graña and Polchinski. The idea is to begin with the D3 brane action of the form $$ ds^2 = Z^{-1/2}\eta_{\mu\nu}dx^\mu dx^\nu + ...
0
votes
0answers
27 views

How can a string “shield” a tear in a flop transition? Can our expanded dimensions tear?

I have read recently that in a process called flop transition in calabi yau dimensions space actually tears and is then somehow "fixed" to create a new shape of Calabi Yau dimension. If a string wraps ...
1
vote
1answer
44 views

Superstring vacuum amplitude on the torus

My question is how to obtain the superstring (Type II A and B) vacuum amplitudes on a torus. They are given in Polchinski's String Theory Vol. 2 equation (10.7.9): ...
0
votes
1answer
71 views

Brane polarisation (Myers Effect/Polchinski-Strassler/KPV)

I have a question about brane polarisation. In the most famous cases I know of--the original giant D2 brane of Myers, the Polchinski-Strassler resolution of the $\mathcal{N}=1^*$ IR singularity, and ...
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0answers
40 views

Abelian and non-Abelian T-duality

What are the advantages and the troubles of performing an Abelian and a non-Abelian T-duality over a type IIB/IIA solution? I have seen that Maldacena and Alday found some correspondence between the ...
0
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0answers
40 views

Books or papers recommendation on orbifold and CFT [duplicate]

Could you recommend some references on orbifold CFT? I have found this paper "The conformal field theory of orbifolds"(1987)(http://inspirehep.net/record/230342) is very useful for me, so I want to ...
1
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1answer
30 views

Why does this allegedly Hermitian Kähler metric have non-zero diagonal terms?

In string theory, the Kähler potential of Kähler moduli (e.g. - the volume of a Calabi-Yau manifold) is given by (see, for instance, Becker, Becker, Schwarz: "String Theory and M Theory" p. 498) $$K ...
0
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0answers
66 views

Kähler Potential of Calabi-Yau volume

At tree level, the Kähler potential is given by (neglecting complex structure) $K = -\ln(-\mathrm{i}(\tau - \bar{\tau})) - 2\ln(V_{CY})$ where $V_{CY} = \frac{1}{6} \kappa_{abc}t^at^bt^c$ ia the the ...
12
votes
8answers
4k views

Why are extra dimensions necessary?

Some theories have more than 4 dimensions of spacetime. But we only observe 4 spacetime dimensions in the real world, cf. e.g. this Phys.SE post. Why are the theories (e.g. string theory) that ...