Abstract
The D1D5P system has a large set of BPS states at its orbifold point. Perturbing away from this ‘free’ point leads to some states joining up into long supermultiplets and lifting, while other states remain BPS. We consider the simplest orbifold which exhibits this lift: that with N = 2 copies of the free c = 6 CFT. We write down the number of lifted and unlifted states implied by the index at all levels upto 6. We work to second order in the perturbation strength λ. For levels upto 4, we find the wavefunctions of the lifted states, their supermultiplet structure and the value of the lift. All states that are allowed to lift by the index are in fact lifted at order O(λ2). We observe that the unlifted states in the untwisted sector have an antisymmetry between the copies in the right moving Ramond ground state sector, and extend this observation to find classes of states for arbitrary N that will remain unlifted to O(λ2).
Highlights
Black holes in string theory must be made by taking bound states of objects — strings and branes — present in the theory
We note that there are many earlier works that study conformal perturbation theory, the lifting of the states, the acquiring of anomalous dimensions, and the issue of operator mixing, in particular in the context of the D1D5 conformal field theory (CFT) see for example [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]
The most basic quantity we can study under such a perturbation is the energy levels of states in the CFT as a function of the perturbation parameter λ
Summary
Black holes in string theory must be made by taking bound states of objects — strings and branes — present in the theory. We observe that if the right moving sector is antisymmetric in the two copies, the state will remain unlifted at O(λ2) We extend this observation to the case N > 2, including the situation where the component strings that are joined may have windings k1, k2 greater than unity. We note that there are many earlier works that study conformal perturbation theory, the lifting of the states, the acquiring of anomalous dimensions, and the issue of operator mixing, in particular in the context of the D1D5 CFT see for example [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. For more computations in conformal perturbation theory in two and higher dimensional CFTs see, e.g. [36,37,38,39,40,41,42,43,44,45,46,47]
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