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A simple question about equation of motion in polchinski's String theory?

In page 14 to get the equation of motion, it takes the variation of the action $$ S_P[X,\gamma]=-\frac{1}{4\pi\alpha'}\int_Md\tau d\sigma(-\gamma)^{1/2}\gamma^{ab}\partial_a X^\mu\partial_b X_\mu $$ ...
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0answers
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Idea behind boundary states in BCFT

In Blumenhagen's book on CFT, in the BCFT chapter he introduces the concept of a boundary state. TO do this, he first explains how there is a duality between the one-loop open string worldsheet and ...
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1answer
64 views

Mass formula for open string with mixed boundary conditions

I want to give an expression for the mass formula of an open string with has Neumannn condtion in $m$ directions and Dirichlet in $n$ directions $X^{i}(\sigma ^{1}=0)=x_{0}^{i}, X^{i}(\sigma ^{1}=\pi)=...
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1answer
53 views

Question about Mode expansion of free compact boson

$(1+1)$-Dim free compact boson, Lagrangian is $$\mathcal{L}= \frac{1}{2}(\partial_\mu\phi(\sigma,t))^2$$ with $\phi(x,t)\sim\phi(x,t)+2\pi r$ and periodic boundary condition along $x$, i.e. $\phi(\...
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0answers
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Differentiating D3 brane worldvolume theories with NS5 brane and NS5 antibrane boundary conditions

In 'Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory', Gaiotto and Witten derive boundary conditions for the worldvolume theory of the D3 brane. In particular the boundary conditions (...
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0answers
151 views

On the boundary conditions for closed and open strings

In the process of finding the equations of motion for a string from the Polyakov action (say in the conformal gauge), we have to implement some boundary conditions on the target spacetime coordinates $...
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1answer
156 views

Gamma matrices in Gaiotto-Witten analysis of N=4 Super Yang-Mills boundary conditions

In the paper Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory by Gaiotto and Witten, an in-depth analysis of supersymmetric boundary conditions in N=4 Super Yang-Mills in four ...
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0answers
47 views

Elliptic genus on torus

The elliptic genus, in defined as $$ \mathcal{E}=\text{Tr}\,q^{L_0-\frac{c}{24}}\bar{q}^{\bar{L}_0-\frac{c}{24}}y^{\alpha J^3} $$ can be computed as a path integral with different boundary ...
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0answers
47 views

What are the boundary conditions for D4-branes ending on D8-branes?

In a recent paper by Cordova and Jafferis, they perform the physical derivation of the AGT correspondence. A crucial step is recognizing that the appropriate boundary conditions for the 5D super Yang-...
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0answers
52 views

Why boundary conditions of an open string involve the time derivative?

I am trying to understand the boundary conditions of an open string stretching from one brane to another, in TIIA theory. Let's consider to D6-branes which spans a line along the $(x_4,x_5)$ plane ...
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2answers
236 views

Poincare invariance of Dirichlet and Neumann boundary conditions

The action which describes a string propagating in a $D$ dimensional spacetime, with given metric $g_{\mu\nu}$, is given by the Polyakov action $$S_{\text{p}}=-\frac{T}{2}\int \mathrm{d}\sigma\mathrm{...
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1answer
116 views

Using the open strings endpoints' boundary conditions and then obtain the EOM

In Zweibach's A first course in string theory, he used the least action principle to get the equations of motion for strings, wehre the variation of action(which should be zero) is : $$\delta S = \...
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1answer
130 views

A question about the antiperiodic conditions in string theory [closed]

We know that for both bosonic and fermionic strings, there are possibly antiperiodic boundary conditions: $$X^\mu(\tau,\sigma+2\pi)=-X^\mu(\tau,\sigma); \tag 1\\$$ $$\Psi(\tau,\sigma+2\pi)=-\Psi(\tau,\...
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1answer
611 views

Boundary Conditions For Strings? [closed]

There seems to be two main boundary conditions for Strings. 1. Neumann Condition: Ends of Strings are free to move up or down. 2. Dirichlet Condition: Ends of Strings are fixed. What other ...
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0answers
161 views

on fundamental 2D conductivity equation boundary value problem

Consider the following homogeneous boundary value problem for a function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/nductivity $\gamma(x+...
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2answers
217 views

Dirichlet boundary conditions in space-time?

In the context of string theory, and world sheets the Dirichlet boundary conditions can be written as: $$\frac{\partial X^\mu(\tau,\sigma_1)}{\partial \tau}=0$$ where $\sigma_1$ is the value of the ...
3
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2answers
401 views

Idea behind Compactified Boson

On p. 167 of his Conformal Field Theory, Di Francesco introduces "Compactified Boson". He says: The invariance of the free-boson Lagrangian [...] with respect to translations $\varphi(x) \...
2
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1answer
120 views

String boundary conditions

I'm reading Polchinski and am confused about equation (1.3.13), $$\gamma_{\tau\sigma}\partial_\tau X^\mu-\gamma_{\tau\tau}\partial_\sigma X^\mu=0~~~~~\text{at}~~~~~\sigma=0,l.$$ It says that this ...
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1answer
389 views

A question about Poincare invariance of Polyakov action

I have a question the variation of the Polyakov action, related to this Phys.SE post. For Polyakov action $$ S_p[X,\gamma]=-\frac{1}{4 \pi \alpha'} \int_{-\infty}^{\infty} d \tau \int_0^l d \sigma (...
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1answer
1k views

Neumann boundary condition and the open string

In string theory, If an open string obeys the Neumann boundary condition, then in the static gauge, one can show that the end points move at the speed of light. The derivation is straightforward, but ...
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1answer
807 views

Do Neveu-Schwarz conditions make sense?

When putting fermions on the string, we have to choose boundary conditions for our spinor fields - Ramond or Neveu-Schwarz. NS conditions on the closed string have antiperiodic conditions such as $\...