49 research outputs found
On the spectrum of AdS₃ × S³× T⁴ strings with Ramond–Ramond flux
No full textWe analyze the spectrum of perturbative closed strings on AdS₃ × S³× T⁴ with Ramond–Ramond flux using integrable methods. By solving the crossing equations we determine the massless and mixed-mass dressing factors of the worldsheet S matrix and derive the Bethe equations. Using these, we construct the underlying integrable spin chain and show that it reproduces the reducible spin chain conjectured at weak coupling in Olof Ohlsson S, Bogdan S Jr and Torrielli A 2013 (arXiv:1211.1952). We find that the string-theory massless modes are described by gapless excitations of the spin chain. The resulting degeneracy of vacua matches precisely the protected supergravity spectrum found by de Boer
Protected string spectrum in AdS(3)/CFT2 from worldsheet integrability
No full textWe derive the protected closed-string spectra of AdS3/CFT2 dual pairs with 16 supercharges at arbitrary values of the string tension and of the three-form fluxes. These follow immediately from the all-loop Bethe equations for the spectra of the integrable worldsheet theories. Further, representing the underlying integrable systems as spin chains, we find that their dynamics involves length-changing interactions and that protected states correspond to gapless excitations above the Berenstein-Maldacena-Nastase vacuum. In the case of AdS3 × S3 × T4 the degeneracies of such operators precisely match those of the dual CFT2 and the supergravity spectrum. On the other hand, we find that for AdS3 × S3 × S3 × S1 there are fewer protected states than previous supergravity calculations had suggested. In particular, protected states have the same su(2) charge with respect to the two three-spheres
The complete worldsheet S matrix of superstrings on AdS3×S3×T4 with mixed three-form flux
No full textWe determine the off-shell symmetry algebra and representations of Type IIB superstring theory on AdS3×S3×T4 with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory
The complete AdS3 ×S3 × T4 worldsheet S matrix
No full textWe derive the non-perturbative worldsheet S matrix for fundamental excitations of Type IIB superstring theory on AdS3 ×S3 × T4 with Ramond-Ramond flux. To this end, we study the off-shell symmetry algebra of the theory and its representations. We use these to determine the S matrix up to scalar factors and we derive the crossing equations that these scalar factors satisfy. Our treatment automatically includes fundamental massless excitations, removing a long-standing obstacle in using integrability to study the AdS3/CFT2 correspondence
The low-energy limit of AdS(3)/CFT2 and its TBA
No full textWe investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states
Protected states in AdS3 backgrounds from integrability
No full textWe write down the algebraic Bethe ansatz for string theory on AdS3 × S3 × T4 and AdS3 × S3 × K3 in its orbifold limits. We use it to determine the wave-functions of protected closed strings in these backgrounds and prove that their energies are protected to all orders in α'. We further apply the ABA to find the wave functions of protected states of AdS3 × S3 × S3 × S1 and its Z2 orbifold. Our findings match with protected spectrum calculations from supergravity, SymN orbifolds and apply to the complete moduli space of these theories, excluding orbifold blow-up modes for which further analysis is necessary
Quantum Spectral Curve for AdS(3)/CFT2: a proposal
No full textWe conjecture the Quantum Spectral Curve equations for string theory on AdS3 × S3 × T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC
The effectiveness of relativistic invariance in AdS(3)
No full textWe use relativistic invariance to investigate two aspects of integrable AdS3 string theory. Firstly, we write down the all-loop TBA equations for the massless sector of the theory with R-R flux, using the recently discovered hidden relativistic symmetry. Secondly, for the low-energy relativistic limit of the theory with NS-NS flux we write down the S matrix, dressing factors and TBA. We find that the integrable system coincides with a restriction to AdS3 of the relativistic q-deformed AdS5 theory. We also comment on the relativistic limit of the small-k NS-NS theory
The evolution of roman frontier defence systems and fortifications the lower danube provinces in the first and second centuries AD
No full textThe defence of the Roman Empire from barbarian attacks depended on two distinct but interrelated features: the actual fortifications on the borders of the imperial provinces and the troops that garrisoned them. The main aim of this dissertation is to provide a collective analysis of Roman defence systems on the Lower Danube region, i.e. the provinces of Pannonia Inferior, Moesia Superior, Moesia Inferior and Dacia. The period of study spans from the early first century to the middle of the second century AD, a period which corresponds to the gradual emergence and final consolidation of the Roman frontier defence systems in the area. On the basis of the physical evidence that has survived from the frontier fortifications of the Lower Danube area, this study attempts to present a reconstruction of the strategic and tactical situation on the frontier and to provide some fresh observations on the motives behind the creation, purpose and function of Roman frontiers during the early Principate. After a brief introduction on some of the views that have been put forward on the subject, the main part of the thesis is divided into four separate chapters, one for each of the provinces studied. These chapters study the fortifications themselves in order to establish their date and garrison so as to offer an evaluation of the characteristic features of the defensive system of each frontier sector. The last chapter brings together the above information in order to produce some conclusions on the defence systems in the area, especially in relation to the rationale behind their creation and subsequent development
Closed Strings and Moduli in AdS3/CFT2
No full textString theory on AdS3×S3×T4 has 20 moduli. We investigate how the perturbative closed string spectrum changes as we move around this moduli space in both the RR and NSNS flux backgrounds. We find that, at weak string coupling, only four of the moduli affect the energies. In the RR background the only effect of these moduli is to change the radius of curvature of the background. On the other hand, in the NSNS background, the moduli introduce worldsheet interactions which enable the use of integrability methods to solve the spectral problem. Our results show that the worldsheet theory is integrable across the 20 dimensional moduli space
